Uniform Accelerated Motion. 6 th Year. Applied Maths Higher Level Kieran Mills

Size: px
Start display at page:

Download "Uniform Accelerated Motion. 6 th Year. Applied Maths Higher Level Kieran Mills"

Transcription

1 6 h Year Applied Mahs Higher Level Kieran Mills Uniform Acceleraed Moion No par of his publicaion may be copied, reproduced or ransmied in any form or by any means, elecronic, mechanical, phoocopying, recording, or oherwise, wihou prior wrien permission from The Dublin School of Grinds. Ref: 6/appmahs/h/km/UAM noes

2 EASTER REVISION COURSES Looking o maximise your CAO poins? Easer is well known as a ime for sudens o vasly improve on he poins ha hey received in heir mock exams. To help sudens ake advanage of his valuable ime, The Dublin School of Grinds is running inensive exam-focused Easer Revision Courses. Each course runs for five days (90 minues per day). The focus of hese courses is o maximise sudens CAO poins. Special offer: Buy s course and ge nd course free. To avail of his offer, early booking is required as courses were fully booked las year. Wha do sudens ge a hese courses? EASTER REVISION COURSE FEES: PRICE TOTAL SAVINGS s Course nd Course FREE rd Course h Course h Course h Course ,075 7h Course ,70 8h Course ,465 9h Course ,660 NOTE: Any bookings for Junior Cer courses will also receive a weekly grind in one subjec for he res of he academic year, free of charge. This offer applies o 3rd and nd year sudens ONLY. FREE DAILY BUS SERVICE For full informaion on our Easer bus service, see 3 pages ahead minues of inensive uiion per day for five days, wih Ireland s leading eachers. Oral Preparaion Courses 99 Comprehensive sudy noes. Separae o he Easer Revision Courses, The Dublin School of Grinds is also running Oral Preparaion Courses. Wih he Oral marking componen of he Leaving Cerificae worh up o 40%, i is of paramoun imporance ha sudens are fully prepared for hese examinaions. These courses will show sudens how o lead he Examiner owards opics ha he suden is prepared in. This will provide sudens wih he confidence hey need o perform a heir peak. 99 A focus on simple shorcus o raise sudens grades and exploi he criically imporan marking scheme. 99 Access o a free supervised sudy room. 99 Access o food and beverage faciliies. NOTE: These courses are buil on he fac ha here are cerain predicable rends ha appear and reoccur over and over again in he Sae Examinaions. ORAL PREPARATION COURSE FEES: PRICE To book, call us on or book online a TOTAL SAVINGS s Oral Course nd Oral Course

3 Timeable An exensive range of course opions are available over a wo-week period o caer for sudens imeable needs. Courses are held over he following weeks:»» Monday s March Friday 5h March 06»» Monday 8h March Friday s April 06 All Easer Revision Courses ake place in The Talbo Hoel, Sillorgan (formerly known as The Sillorgan Park Hoel). 6h Year Easer Revision Courses SUBJECT LEVEL DATES TIME Accouning H Monday s March Friday 5 h March 8:00am - 9:30am Agriculural Science H Monday 8 h March Friday s April :00pm - 3:30pm Applied Mahs H Monday 8 h March Friday s April 8:00am - 9:30am Ar Hisory H Monday 8 h March Friday April 8:00am - 9:30am Biology Course A* H Monday s March Friday 5 h March 8:00am - 9:30am Biology Course A* H Monday s March Friday 5 h March :00pm - :30pm Biology Course A* H Monday 8 h March Friday s April 0:00am - :30am Biology Course B* H Monday s March Friday 5 h March 0:00am - :30am Biology Course B* H Monday s March Friday 5 h March :00pm - 3:30pm Biology Course B* H Monday 8 h March Friday s April 8:00am - 9:30am Business H Monday s March Friday 5 h March :00pm - :30pm Business H Monday 8 h March Friday s April 8:00am - 9:30am Chemisry Course A* H Monday 8 h March Friday s April :00pm - :30pm Chemisry Course B* H Monday 8 h March Friday s April :00pm - 3:30pm Classical Sudies H Monday s March Friday 5 h March 8:00am - 9:30am Economics H Monday s March Friday 5 h March 8:00am - 9:30am Economics H Monday 8 h March Friday s April 0:00am - :30am English Paper * H Monday s March Friday 5 h March :00pm - :30pm English Paper * H Monday s March Friday 5 h March 0:00am - :30am English Paper * H Monday s March Friday 5 h March :00pm - 3:30pm English Paper * H Monday 8 h March Friday s April 0:00am - :30am English Paper * H Monday 8 h March Friday s April :00pm - :30pm French H Monday s March Friday 5 h March 0:00am - :30am French H Monday 8 h March Friday s April 8:00am - 9:30am Geography H Monday 8 h March Friday s April 8:00am - 9:30am Geography H Monday 8 h March Friday s April 0:00am - :30am German H Monday s March Friday 5 h March 0:00am - :30am Hisory (Europe)* H Monday s March Friday 5 h March :00pm - 3:30pm Hisory (Ireland)* H Monday s March Friday 5 h March :00pm - :30pm Home Economics H Monday s March Friday 5 h March 0:00am - :30am Irish H Monday s March Friday 5 h March 0:00am - :30am Irish H Monday 8 h March Friday s April :00pm - :30pm Mahs Paper * H Monday s March Friday 5 h March 8:00am - 9:30am Mahs Paper * H Monday s March Friday 5 h March :00pm - :30pm Mahs Paper * H Monday 8 h March Friday s April 0:00am - :30am Mahs Paper * H Monday 8 h March Friday s April :00pm - 3:30pm Mahs Paper * H Monday s March Friday 5 h March 0:00am - :30am Mahs Paper * H Monday s March Friday 5 h March :00pm - 3:30pm Mahs Paper * H Monday 8 h March Friday s April :00pm - :30pm Mahs Paper * H Monday 8 h March Friday s April 4:00pm - 5:30pm Mahs O Monday s March Friday 5 h March 8:00am - 9:30am Mahs O Monday 8 h March Friday s April :00pm - :30pm Physics H Monday 8 h March Friday s April 0:00am - :30am Spanish H Monday s March Friday 5 h March :00pm - 3:30pm Spanish H Monday 8 h March Friday s April 0:00am - :30am * Due o large course conen, hese subjecs have been divided ino wo courses. For a full lis of opics covered in hese courses, please see 3 pages ahead. 6h Year Oral Preparaion Courses SUBJECT LEVEL DATES TIME French H Sunday 0 h March 0:00am - :00pm German H Saurday 6 h March 0:00am - :00pm Irish H Saurday 6 h March 0:00am - :00pm Spanish H Saurday 9 h March :00pm - 5:00pm 5h Year Easer Revision Courses SUBJECT LEVEL DATES TIME Mahs H Monday 8 h March Friday s April 8:00am - 9:30am English H Monday 8 h March Friday s April 4:00pm - 5:30pm Noe: 5h year sudens are welcome o aend any 6h year course as par of our buy ge free offer. 3rd Year Easer Revision Courses SUBJECT LEVEL DATES TIME Business Sudies H Monday 8 h March Friday s April 8:00am - 9:30am English H Monday s March Friday 5 h March 8:00am - 9:30am English H Monday 8 h March Friday s April :00pm - 3:30pm French H Monday 8 h March Friday s April :00pm - :30pm Geography H Monday 8 h March Friday s April :00pm - :30pm German H Monday s March Friday 5 h March 8:00am - 9:30am Hisory H Monday s March Friday 5 h March 4:00pm - 5:30pm Irish H Monday 8 h March Friday s April :00pm - 3:30pm Mahs H Monday s March Friday 5 h March 0:00am - :30am Mahs H Monday s March Friday 5 h March :00pm - :30pm Mahs H Monday 8 h March Friday s April 0:00am - :30am Mahs O Monday 8 h March Friday s April :00pm - :30pm Science H Monday 8 h March Friday s April :00pm - 3:30pm Science H Monday s March Friday 5 h March :00pm - 3:30pm Spanish H Monday s March Friday 5 h March :00pm - :30pm nd Year Easer Revision Courses SUBJECT LEVEL DATES TIME Mahs H Monday s March Friday 5 h March :00pm - 3:30pm BUY ST COURSE GET ND COURSE FREE! NOTE: Any bookings for Junior Cer courses will also receive a weekly grind in one subjec for he res of he academic year, free of charge. This offer applies o 3rd and nd year sudens ONLY. BOOK EARLY TO AVAIL OF THE SPECIAL OFFER

4 Conens: Uniform Acceleraed Moion Secion Using he Formulae... Exercise...6 Exercise...8 Secion Successive Times and Disances...0 Exercise Secion 3 Cach-up Problems...6 Exercise Secion 4 Velociy-ime Graphs...8 Exercise Secion 5 Free-fall...4 Exercise Leaving Cer Quesions The Dublin School of Grinds Page Kieran Mills & Tony Kelly

5 The Dublin School of Grinds Page Kieran Mills & Tony Kelly Secion : Using he Formulae 0 m = 0 s a = 4 m s - Quaniy Symbol Unis Acceleraion a m s Iniial velociy u m s Final velociy v m s Time s Displacemen s m - Lef s = 300 m Equaions of Moion Ex. How long does i ake he bus o ravel from A o B? How far is i from A o B? Soluion a = 4 ms u = 0 ms v = 50 ms =? + Righ +a: acceleraion a: deceleraion A B u = 0 m s - v = 50 m s - v= u+ a 50 = = 4 = 0 s v= u+ a...( )[ No No s] s= ( v+ u )...( )[ a] s= u+ a...( 3)[ No v] v = u +as...( 4)[ No No ] s= v a...( 5)[ u] s= ( v+ u ) = ( )( 0) = ( 60)( 0) = 300 m

6 The Dublin School of Grinds Page 3 Kieran Mills & Tony Kelly Example u = 3 m s, a = 6 m s, = 4 s, s =? Example u = 6 m s, a = 0 m s, = 4 s, v =? Example 3 u = 8 m s, v = 5 m s, = 6 s, s =? Example 4 u = 4 m s, v = 9 m s, a = 0.5 m s, s =? Example 5 s = 0 m, v = 0 m s, = 3 s, a =? Example 6 s = 8 m, u = 6 m s, a = m s, =?

7 The Dublin School of Grinds Page 4 Kieran Mills & Tony Kelly Example u = 3 m s, a = 6 m s, = 4 s, s =? Soluion Mahemaical Calculaions u = 3 m s a = 6 m s = 4 s s =? No v presen. Use Equaion (3). s= u+ a = ()( 3 4) + ( 6)( 4) = + 48 = 60 m Example u = 6 m s, a = 0 m s, = 4 s, v =? Soluion Mahemaical Calculaions u = 6 m s a = 0 m s = 4 s v =? No s presen. Use Equaion (). v= u+ a = ( ) = = 46 ms Example 3 u = 8 m s, v = 5 m s, = 6 s, s =? Soluion Mahemaical Calculaions u = 8 m s v = 5 m s = 6 s s =? No a presen. Use Equaion (). s= ( v+ u ) = ( ) = 33 ( ) = 69 m

8 The Dublin School of Grinds Page 5 Kieran Mills & Tony Kelly Example 4 u = 4 m s, v = 9 m s, a = 0.5 m s, s =? Soluion Mahemaical Calculaions u = 4 m s v = 9 m s a = 0.5 m s s =? No presen. Use Equaion (4). v = u + as 9 = (. ) s 8 = 6 + s s = 65 m Example 5 s = 0 m, v = 0 m s, = 3 s, a =? Soluion Mahemaical Calculaions s = 0 m v = 0 m s = 3 s a =? No u presen. Use Equaion (5). s= v a 0 = 0() 3 a() = 30 a 40 = 60 9a 9a = 80 a = 0 ms Example 6 s = 8 m, u = 6 m s, a = m s, =? Soluion Mahemaical Calculaions s = 8 m u = 6 m s a = m s =? No v presen. Use Equaion (3). s= u+ a 8= ( 6) + ( ) 8= = 0 ( 4)( ) = 0 = s, 4s

9 Exercise. Using he formulae. u = 0 m s, a= 4 m s, = 6 s, s =?. u = 5 m s, a= 3 m s, = 3 s, v=? 3. u = 0 m s, a= 4 m s, = 4 s, s =? 4. u = 7 m s, v= 5 m s, = 0 s, s =? 5. u = 4 m s, v= 0 m s, s = 7m, a =? 6. v= 30 m s, a = 6 m s, = s, u =? 7. u = 6 m s, v= 3 m s, s = 5. m, a =? 8. s = 35 m, a= 6 m s, = s, u =? 9. s = u = 40 m, 5 m s, v= 5 m s, =? 0. u = 5 m s, v= 0 m s, a = 0. 5 m s, s =?. u = 48 m s, v= m s, = 9 s, a =?. s = 30 m, = s, a = 4 m s, v=? 3. s = 0 m, = 3 s, v= 0 m s, a=? 4. s = a= 4 m, m s, v= 3 m s, =? 5. s = v= 8 m, 7 m s, a = 3 m s, =? 6. s = u = 4 m, 5 m s, a= m s, =? 7. s = u = 8 m, 6 m s, a= m s, =? 8. v= 7 km h, a = 05. m s, = min, u =? 9. s = v= 8 m, 8 m s, a= 3m s, u =? 0. s = v= 6 m, 4 m s, a= 4 m s, =? The Dublin School of Grinds Page 6 Kieran Mills & Tony Kelly

10 Answers Exercise. 7 m. 4 m s 3. 3 m 4. 0 m. 4 m s. 9 m s 3. 0 m s 4. 4 s 5. 6 m s 6. 8 m s 7. 9 m s 8 5. s, s 7. s, 4s s 8..5 m s 9. 4 s m 8. 0 m s 9. 4 m s 0. 3 s The Dublin School of Grinds Page 7 Kieran Mills & Tony Kelly

11 Exercise. Simple problems using he formulae. A rain sars from res and acceleraes uniformly a.5 m s unil i reaches a speed of 5 m s. Find he disance moved and he ime aken for his moion.. A car can accelerae from res o 90 km h in 7.5 seconds. Find is acceleraion. 3. In ravelling 65 cm along he barrel of a rifle a bulle acceleraes from res o 30 m s. Find he accceleraion and he ime he bulle is in he barrel. 4. A car ravelling a 4 m s requires a minimum braking disance of 36 m. Wha is is deceleraion? How long does i ake o sop? 5. A car sars from res wih acceleraion 4 m s. How far does i go in (i) s, (ii) 3 s, (iii) he hird second. 6. A body moves in a sraigh line and increases is velociy from 3 m s o 5 m s uniformly in 6 s. Find he acceleraion and he disance ravelled. 7. A paricle sars wih a velociy of 3 m s and acceleraes uniformly a.5 m s. How far does i go in (i) s, (ii) 5 s, (iii) he fourh second. 8. A body is projeced from he origin wih a velociy of 8 m s and acceleraion m s. Find (i) he velociy when = 3 s, (ii) when i comes o insananeous res. 9. A paricle moves along a sraigh line beween wo poins P and Q wih consan acceleraion 0.8 m s. Is velociy a Q is. m s greaer han he velociy a P. If he disance PQ is 48 m, find he velociy a P. How long afer passing P does i ake he velociy o reach 48 m s. 0. A car is moving wih speed u m s. The brakes of he car can produce a consan deceleraion of 5 m s. I is known ha when he driver decides o sop, a period of 5 s elapses before he brakes are applied. As he car passes a poin O, he driver decides o sop. Find in erms of u he minimum disance of he car from O when he car comes o res. The driver is approaching raffic lighs and is 0 m away when he ligh changes from green o amber. The lighs remain amber for 3 s before changing o red. Show (a) when u < 30 he driver can sop before reaching he lighs, (b) when u > 34 he driver can pass he ligh before i urns red. The Dublin School of Grinds Page 8 Kieran Mills & Tony Kelly

12 Answers Exercise. 5 m, 0 s. 0 3 ms 3. 40, 69 m s, s 4. 8 m s, 3 s 5. 8 m, 8 m, 0 m 6. m s, 54 m m, m, 8.5 m 8. m s, 4 s m s, 0.75 s 0. 0 u + 5 u The Dublin School of Grinds Page 9 Kieran Mills & Tony Kelly

13 The Dublin School of Grinds Page 0 Kieran Mills & Tony Kelly Secion : Successive Times and Disances Example In wo successive seconds a uniformly acceleraing body ravels 5 m and 3 m. Find is acceleraion and is iniial velociy. Example A uniformly deceleraing body covers successive 00 m disances in 5 s and 0 s. Find is iniial speed, he deceleraion and he furher ime for he body o come o res.

14 The Dublin School of Grinds Page Kieran Mills & Tony Kelly Example In wo successive seconds a uniformly acceleraing body ravels 5 m and 3 m. Find is acceleraion and is iniial velociy. Soluion In hese ypes of problems always use he equaion shown. Take all values from he beginning poin. u 5= u() + a() 5 = u+ a 0 = u+ a...( ) = s a s= u+ a = s, s = 8 m = s s = 5 m s = 3 m 8 = u( ) + a( ) 8 = u+ a...( ) Mahemaical Calculaions 0 = u+ a...( )( ) 8 = u+ a...( ) 0 = u a 8 = u+ a 8 = a 0 = u+ a...( ) 0 = u + 8 = u u = Answers a= 8 ms, u = ms

15 Con... The Dublin School of Grinds Page Kieran Mills & Tony Kelly Example A uniformly deceleraing body covers successive 00 m disances in 5 s and 0 s. Find is iniial speed, he deceleraion and he furher ime for he body o come o res. Soluion u In hese ypes of problems always use he equaion shown. Take all values from he beginning poin. 00 = u() 5 + a() = 5u+ a 40 = u+ 5a...( ) = 5 s a s= u+ a s = 00 m s = 00 m = 5 s, s = 00 m 00 = u( 5) + a( 5) 5 00 = 5u+ a 80 = 6u+ 45a...( ) = 0 s =? 0 m s - Mahemaical Calculaions 40 = u+ 5a...( )( 3) 80 = 6u+ 45a...( ) 0 = 6u 5a 80 = 6u + 45a 40 = 30a 40 = u+ 5a...( ) 4 40 = u + 5( 3) 0 40 = u 3 0 = 6u 0 40 = 6u = u 40 6 u = ms 70 3

16 The Dublin School of Grinds Page 3 Kieran Mills & Tony Kelly Example A uniformly deceleraing body covers successive 00 m disances in 5 s and 0 s. Find is iniial speed, he deceleraion and he furher ime for he body o come o res. Soluion u = 5 s a s= u+ a s = 00 m s = 00 m = 5 s, s = 00 m Mahemaical Calculaions Furher ime for body o come o res: u = 70 3 a = 4 3 ms v = 0 ms =? ms v= u+ a = 3 + ( 3) = 3 4 = = = 7. 5 s = 0 s =? Answer: Furher ime = =.5 s 4 0 m s - Mahemaical Calculaions 40 = u+ 5a...( )( 3) 80 = 6u+ 45a...( ) 0 = 6u 5a 80 = 6u + 45a 40 = 30a 40 = u+ 5a...( ) 4 40 = u + 5( 3) 0 40 = u 3 0 = 6u 0 40 = 6u = u 40 6 u = ms 70 3

17 Exercise 3. Successive Times/Successive Disances. In wo successive seconds a uniformly acceleraing body ravels 4 m and 8 m. Find is acceleraion.. A uniformly acceleraing body ravels 5 m and m repecively in is firs wo seconds. How far does i ravel in he fourh second? 3. A uniformly deceleraing body covers successive 00 m disances in 5 s and 0 s. Find is iniial speed, he deceleraion and he furher ime for he body o come o res. 4. A paricle sars from res and moves in a sraigh line wih uniform acceleraion. I passes hree poins A, B and C where AB =05 m and BC = 63 m. If i akes 6 s o ravel from A o B and s from B o C find (i) is acceleraion, (ii) he disance of A from he saring posiion. 5. A spriner runs a race wih consan acceleraion hroughou. During he race he passes four poss A, B, C, D such ha AB = BC = CD = 36 m. If he spriner akes 3 s o run from A o B and s o run from B o C, how long does i akes o run from C o D? 6. A paricle moving in a sraigh line wih uniform acceleraion describes 3 m in he fifh second of is moion and 3 m in he sevenh second. Calculae is iniial velociy. 7. A body ravels in a sraigh line wih uniform acceleraion. The paricle passes hree poins A, B and C a = 0, = 3 s and = 6 s. If BC = 90 m and he speed of he paricle a B is m s, find he acceleraion of he body and is speed a A. 8. A, B, C are hree poins which lie in ha order on a sraigh road wih AB = 45 m and BC = 3 m. A car ravels along he road in he direcion ABC wih consan acceleraion f. The car passes A wih speed u and passes B five seconds laer and passes C wo seconds afer ha. Find u and f. 9. A car is moving along a a seady 0 m s when he driver suddenly sees a ree across he road 56 m ahead. He immediaely applies he brakes giving he car a consan deceleraion of 4 m s. How far in fron of he ree does he car come o res? If he driver had no reaced immediaely and he brakes were applied one second laer wih wha speed would he car have hi he ree? 0. A, B, C are hree poins on a sraigh line in ha order. A body is projeced from B owards A wih a speed of 5 m s. The body experiences an acceleraion of m s owards C. If BC = 4 m, find he ime o reach C, and he disance ravelled by he body from he insan of projecion unil i reaches C.. A bus.5 m long ravels wih consan acceleraion. The fron of he bus passes a poin P wih speed u and he rear passes P wih speed v. Find in erms of u and v (i) he ime aken for he bus o pass P, (ii) wha fracion of he bus passes P in half his ime. The Dublin School of Grinds Page 4 Kieran Mills & Tony Kelly

18 . A body moving in a sraigh line wih consan acceleraion passes in succession hrough poins A, B, C and D where AB = x, BC = y and CD = z where he disances x, y and z are covered in equal inervals of ime. Show y = x + z. 3. A uniformly deceleraing rain of lengh 40 m eners a saion of lengh 80 m. The fron engine leaves he saion 5 s laer and he rear of he rain leaves he saion afer a furher 5 s. Find he deceleraion of he rain. 4. A uniformly acceleraing body sars wih a speed of u, in successive imes of ravels disances s and s. Prove ha is acceleraion is 4 u s. 5. A body sars moving in a sraigh line wih velociy u and acceleraion a. If when he velociy has increased o 5u he acceleraion is reversed in direcion is magniude being unalered prove ha when he paricle reurns o is saring poin is velociy will be 7u. Answers Exercise 3. 4 m s. 3 m ms, 3 ms, 5. s 4. (i) 3.5 m s, (ii) 7 m 5..6 s 6. 5 m s 7. 6 m s, 3 m s 8. 4 m s, m s 9. 6 m, 0.6 m s 0. 8 s, 36.5 m 5 3u+ v., v+ u 4( u+ v) 3..6 m s The Dublin School of Grinds Page 5 Kieran Mills & Tony Kelly

19 The Dublin School of Grinds Page 6 Kieran Mills & Tony Kelly Secion 3: Cach-up Problems Example Two bodies sar ogeher a he same ime a he same place and move along he same sraigh line. If one moves wih a consan speed of 6 m s while he oher sars from res and moves a a consan acceleraion of 4 m s. How long will i ake before hey are ogeher? Example Two bodies A and B ravel in he same direcion along he same line. Body A sars wih velociy 5 m s and acceleraion 3 m s. The oher body sars from he same place wih velociy m s and acceleraion 4 m s. Find when and where hey are ogeher again. Example 3 Two bodies move in he same direcion along parallel pahs. A sars from a poin O wih velociy 8 m s and acceleraion m s and B sars 8 m ahead of A and moves off wih velociy m s a acceleraion 4 m s. Find when hey will be ogeher and heir disances from O a hese imes. Wha are heir respecive speeds when hey are ogeher? Example 4 If A sars seconds before B find when and where hey are ogeher. Find he maximum disance ha A moves ahead of B in he subsequen moion. u = 0 m s a = m s A 64 m B u = m s a = 4 m s

20 The Dublin School of Grinds Page 7 Kieran Mills & Tony Kelly Example Two bodies sar ogeher a he same ime a he same place and move along he same sraigh line. If one moves wih a consan speed of 6 m s while he oher sars from res and moves a a consan acceleraion of 4 m s. How long will i ake before hey are ogeher? Soluion = 0 s A B u = 6 m s a = 0 m s u = 0 m s a = 4 m s s= u+ a s = s A B Separaion Equaion: sa sb s s = 6 A B sa = 6+ ( 0) = 6 s = ( 0) + ( 4) B = Mahemaical Calculaions Togeher (level): sa sb =0 6 = 0 6 = 0 8 = 0 ( 8) = 0 = 0 s, 8s Answers A and B are ogeher afer 0 s and afer 8 s.

21 The Dublin School of Grinds Page 8 Kieran Mills & Tony Kelly Example Two bodies A and B ravel in he same direcion along he same line. Body A sars wih velociy 5 m s and acceleraion 3 m s. The oher body sars from he same place wih velociy m s and acceleraion 4 m s. Find when and where hey are ogeher again. Soluion = 0 s A B u = 5 m s a = 3 m s - u = m s a = 4 m s s= u+ a s = s A B Separaion Equaion: sa sb 3 s s = 5+ A B = 3 s = () 5 + () 3 A 3 = 5+ s = ( ) + ( 4) B = + Mahemaical Calculaions Togeher (level): sa sb =0 3 = 0 6 = 0 ( 6) = 0 = 0 s, 6 s A and B are ogeher afer 0 s and afer 6 s. Disance A and B have ravelled afer 6 s: s = B + = 6 ( ) + 6 ( ) = 6 ( ) + 36 ( ) = + 7 = 84 m

22 The Dublin School of Grinds Page 9 Kieran Mills & Tony Kelly Example 3 Two bodies move in he same direcion along parallel pahs. A sars from a poin O wih velociy 8 m s and acceleraion m s and B sars 8 m ahead of A and moves off wih velociy m s a acceleraion 4 m s. Find when hey will be ogeher and heir disances from O a hese imes. Wha are heir respecive speeds when hey are ogeher? Soluion = 0 s o A u = 8 m s a = m s 8 m - s= u+ B sars 8 m ahead of A. Therefore, add a 8 o he disance equaion for B. - B s = s A B u = m s a = 4 m s - - Separaion Equaion: sa sb s s = 8+ 8 A B = s = () 8 + ( ) A = 8+ s = 8+ ( ) + ( 4) B = 8+ + Mahemaical Calculaions Togeher (level): sa sb = = = 0 ( )( 4) = 0 = s, 4 s Con...

23 The Dublin School of Grinds Page 0 Kieran Mills & Tony Kelly Example 3 Two bodies move in he same direcion along parallel pahs. A sars from a poin O wih velociy 8 m s and acceleraion m s and B sars 8 m ahead of A and moves off wih velociy m s a acceleraion 4 m s. Find when hey will be ogeher and heir disances from O a hese imes. Wha are heir respecive speeds when hey are ogeher? Soluion o A u = 8 m s a = m s 8 m - - s= u+ a s = s = 0 m A B B u = m s a = 4 m s - - v A = m s - v B = 0 m s - v= u+ a = 0 s = s = 4 s s = + A () 8 ( ) = 8+ Mahemaical Calculaions Disances and speeds afer s: sa = 8+ = 8 ( ) + ( ) = = 0 m va = u+ a = () 8 + ( )( ) = 8+ 4 = ms v B = u+ a = ( ) + ( 4)( ) = + 8 = 0 ms Con...

24 The Dublin School of Grinds Page Kieran Mills & Tony Kelly Example 3 Two bodies move in he same direcion along parallel pahs. A sars from a poin O wih velociy 8 m s and acceleraion m s and B sars 8 m ahead of A and moves off wih velociy m s a acceleraion 4 m s. Find when hey will be ogeher and heir disances from O a hese imes. Wha are heir respecive speeds when hey are ogeher? Soluion s= u+ a v= u+ a = 0 s = s = 4 s s A = s B = 48 m o A u = 8 m s a = m s 8 m - - s = s = 0 m A B B u = m s a = 4 m s - - sa = () 8 + ( ) = 8+ - v A = m s - v B = 0 m s - v A = 6 m s - v B = 8 m s Mahemaical Calculaions Disances and speeds afer 4 s: sa = 8+ = 84 ( ) + ( 4) = = 48 m va = u+ a = () 8 + ( )( 4) = 8+ 8 = 6 ms vb = u+ a = ( ) + ( 4)( 4) = + 6 = 8 ms

25 The Dublin School of Grinds Page Kieran Mills & Tony Kelly Example 4 If A sars seconds before B find when and where hey are ogeher. Find he maximum disance ha A moves ahead of B in he subsequen moion. Soluion s= u+ a - u = m s - B a = 4 m s 64 m = 0 s If A sars s before B, ake A s ime as ( + ) s and B s ime as s. Mahemaical Calculaions = s s = A ( 0)( ) ( )( ) = 0 s A = sb = ( + ) = 0 - u = 0 m s - A a = m s + = ( 5)( 8) = 0 = = 5s, 8s Separaion Equaion: sa sb s s = A B = s = 64 + B () + ( 4) = Togeher (level): sa sb =0 A and B are ogeher (level) 5 s and 8 s afer B sars. Con...

26 The Dublin School of Grinds Page 3 Kieran Mills & Tony Kelly Example 4 If A sars seconds before B find when and where hey are ogeher. Find he maximum disance ha A moves ahead of B in he subsequen moion. Soluion A s= u+ a ( + ) = s ( + ) = 7 s ( + ) = 0 s s A = s B = 00 m u = 0 m s a = m s - - s = s = 9 m A B + - u = m s - B a = 4 m s 64 m = 0 s s A = s B = = 5 s = 8 s Separaion Equaion: s s = A B Mahemaical Calculaions Disance afer 5 s: sa = = () () + 4 = = 9 m Disance afer 8 s: sa = = () () + 4 = = 00 m Con...

27 The Dublin School of Grinds Page 4 Kieran Mills & Tony Kelly Example 4 If A sars seconds before B find when and where hey are ogeher. Find he maximum disance ha A moves ahead of B in he subsequen moion. Soluion A The maximum separaion occurs when he velociies of A and B are equal. s= u+ a ( + ) = s ( + ) = 7 s ( + ) = 0 s s A = s B = 00 m u = 0 m s a = m s - - s = s = 9 m A B + - u = m s - B a = 4 m s 64 m = 0 s s A = s B = = 5 s = 8 s Separaion Equaion: s s = A B Mahemaical Calculaions Maximum Separaion: va = vb va = u+ a = 0 + ( )( + ) = = + 4 vb = u+ a = + ( 4) = 4 + va = vb + 4 = 4+ 3 = = 65. s s s = A B = ( 65. ) + 3( 65.) 40 = 5. m

28 Exercise 4. Cach up. Two bodies sar ogeher a he same ime a he same place and move along he same sraigh line. If one moves wih a consan speed of 8 m s while he oher sars from res and moves a a consan acceleraion of m s. How long will i ake before hey are ogeher?. A car A passes a poin P on a sraigh road a a consan speed of 0 m s. A he same ime anoher car B sars from res a P wih uniform acceleraion.5 m s. (i) When and how far from P will B overake A. (ii) If B ceases o accelerae on overaking, wha ime elapses beween he wo cars passing a poin Q which is 3 km from P. 3. A boy runs a 4 m s away from a cyclis who sars a res and acceleraes a m s. If he boy has an iniial lead of 5 m, how long does he cyclis ake o cach him? 4. Two bodies A and B ravel in he same direcion along he same line. Body A sars wih velociy 3 m s and acceleraion m s. The oher body sars from he same place wih velociy m s and acceleraion 3 m s. Find when and where hey are ogeher again. 5. Two bodies move along parallel racks in he same direcion. Body A sars wih velociy m s and acceleraion 6 m s. Body B sars from he same place and he same ime wih velociy 5 m s and acceleraion m s. Find when and where hey are ogeher again. Find heir velociies when hey are ogeher for he second ime. 6. Two bodies move in he same direcion along parallel pahs. A sars from poin O wih velociy m s and acceleraion 4 m s. B sars 6 m ahead of A wih velociy 3 m s and acceleraion m s. Find when and where hey are ogeher and heir velociies a his insan. 7. Two bodies move in he same direcion along parallel pahs. A sars from a poin O wih velociy 8 m s and acceleraion m s and B sars 8 m ahead of A and moves off wih velociy m s a acceleraion 4 m s. Find when hey will be ogeher and heir disances from O a hese imes. 8. Two bodies A and B ravel in he same direcion along he same line from he same poin P a he same ime. A sars wih velociy 5 m s and acceleraion 3 m s. B sars wih velociy m s and acceleraion 4 m s. They are ogeher again a poin Q. Find he ime a which hey are ogeher and he disance PQ. Find heir maximum disance apar beween P and Q. 9. Two bodies move in he same direcion along parallel pahs. They sar a he same poin P a he same ime. A sars from P wih velociy 3 m s and acceleraion m s. B sars wih velociy m s and acceleraion 3 m s. They are ogeher again a poin Q. Find he ime a which hey are ogeher and he disance PQ.Find heir maximum disance apar beween P and Q. 0. Two bodies A and B move along parallel sraigh lines in he same direcion from he same poin P. A sars wih velociy 4 m s and acceleraion m s. B sars second afer A wih velociy m s and acceleraion 4 m s. Find when and where hey will be ogeher. The Dublin School of Grinds Page 5 Kieran Mills & Tony Kelly

29 . Two bodies A and B move along parallel sraigh lines in he same direcion from he same poin P. A sars from poin P wih velociy 5 m s and acceleraion 4 m s. B sars second before A wih velociy 6 m s and acceleraion 3 m s from a poin a disance of.5 m o he righ of P. Find when and where hey are ogeher.. Find when and where hey are ogeher. Find heir maximum separaion beween he wo imes when hey are ogeher. A u = 0 m s a = m s B u = m s a = 4 m s 8m 3. If A sars seconds before B find when and where hey are ogeher. Find heir maximum separaion beween he wo posiions. A u = 0 m s a = m s B u = m s a = 4 m s 4. A car A sars from a poin P wih iniial velociy 8 m s and hen ravels wih uniform acceleraion 4 m s. Two seconds laer a second car B sars from P wih an iniial velociy of 30 m s and hen moves wih a uniform acceleraion of 3 m s. Show ha afer passing A, B will never be ahead by more han 74 m. 5. Bodies A and B sar ogeher and move along he same sraigh line. A sars wih a speed of 0 m s and moves wih a consan deceleraion, while B sars a 5 m s and acceleraes a 4 m s. Find he deceleraion of A if hey mee when he velociy of B is wice ha of A. 6. The driver of a car ravelling a 0 m s sees a second car 0 m in fron ravelling in he same direcion a a uniform speed of 8 m s. (a) Wha is he leas uniform reardaion ha mus be applied o he faser car o avoid collision? (b) If he acual reardaion is m s find (i) he ime inerval in seconds for he faser car o reach a poin 66 m behind he slower car, (ii) he shores disance beween he cars. 64 m The Dublin School of Grinds Page 6 Kieran Mills & Tony Kelly

30 Answers Exercise 4. 8 s. (i) 8 s, 80 m (ii) 46 s 3. 5 s 4. 4 s, 8 m from saring poin 5..5 s, 9.75 m, m s, 8 m s 6. 3 s, 4 m, 4 m s, 9 m s 7. s, 4 s, 0 m, 48 m 8. 6 s, 84 m, 4.5 m 9. 4 s, 8 m, m 0. 5 s afer B sars, 60 m. 0 s afer A sars, 50 m from P. s, 8 s,.5 m 3. 5 s and 8 s afer B sars, 9 m from A and 00 m from A,.5 m 5. 4 m s 6. (a) 0.6 m s (b) (i) 6 s, 8 s; (ii) 48 m The Dublin School of Grinds Page 7 Kieran Mills & Tony Kelly

31 The Dublin School of Grinds Page 8 Kieran Mills & Tony Kelly Secion 4: Velociy-ime Graphs Example A car saring from res acceleraes uniformly over 8 s o a velociy of 6 m s. I hen mainains a consan velociy for he nex 0 s. I finally deceleraes uniformly o res for 4 s. Draw a velociy-ime curve o represen he moion of he car. Use he graph o find (i) he acceleraion and disance ravelled by he car in he firs 8 s, (ii) he disance ravelled by he car over he nex 0 s, (iii) he deceleraion and disance ravelled by he car over he las 4 s, (iv) he average velociy of he car for is enire journey. Example A car ravels from A o B. I sars from res a A and acceleraes a m s unil i reaches a speed of 30 m s. I hen ravels a his speed for 600 m and hen deceleraes a.5 m s o come o res a B. Find (i) he oal ime for he journey, (ii) he disance from A o B, (iii) he average speed for he journey. Example 3 A paricle P wih speed 40 m s begins o decelerae uniformly a a cerain insan while anoher paricle Q sars from res 6 s laer and acceleraes uniformly. When he second paricle Q has ravelled 5 m, boh paricles have a speed of 5 m s. (i) Show he moion of boh on he same speed-ime curve. (ii) How many seconds afer he commencemen of deceleraion does he firs paricle P come o res?

32 The Dublin School of Grinds Page 9 Kieran Mills & Tony Kelly Example A car saring from res acceleraes uniformly over 8 s o a velociy of 6 m s. I hen mainains a consan velociy for he nex 0 s. I finally deceleraes uniformly o res for 4 s. Draw a velociy-ime curve o represen he moion of he car. Use he graph o find (i) he acceleraion and disance ravelled by he car in he firs 8 s, (ii) he disance ravelled by he car over he nex 0 s, (iii) he deceleraion and disance ravelled by he car over he las 4 s, (iv) he average velociy of he car for is enire journey. Soluion - v (m s ) (s) Velociy Time Curves Acceleraion = Slope of curve Disance = Area under curve Con...

33 The Dublin School of Grinds Page 30 Kieran Mills & Tony Kelly Example A car saring from res acceleraes uniformly over 8 s o a velociy of 6 m s. I hen mainains a consan velociy for he nex 0 s. I finally deceleraes uniformly o res for 4 s. Draw a velociy-ime curve o represen he moion of he car. Use he graph o find (i) he acceleraion and disance ravelled by he car in he firs 8 s, (ii) he disance ravelled by he car over he nex 0 s, (iii) he deceleraion and disance ravelled by he car over he las 4 s, (iv) he average velociy of he car for is enire journey. Soluion - v (m s ) a = m s - 64 m Run = 8 s Base b = 8 Area of a riangle = bh Rise = 6 m s - Heigh h = 6 (s) Velociy Time Curves Acceleraion a = Slope of curve Disance s = Area under curve Mahemaical Calculaions (i) Rise 6 ms a = = = ms Run 8 s s= bh = ()( 8 6 ) = 64 m Con...

34 The Dublin School of Grinds Page 3 Kieran Mills & Tony Kelly Example A car saring from res acceleraes uniformly over 8 s o a velociy of 6 m s. I hen mainains a consan velociy for he nex 0 s. I finally deceleraes uniformly o res for 4 s. Draw a velociy-ime curve o represen he moion of he car. Use he graph o find (i) he acceleraion and disance ravelled by he car in he firs 8 s, (ii) he disance ravelled by he car over he nex 0 s, (iii) he deceleraion and disance ravelled by he car over he las 4 s, (iv) he average velociy of he car for is enire journey. Soluion - v (m s ) a = m s - Breadh b = 6 64 m 30 m (s) Lengh l = 0 Area of a recangle = l b Velociy Time Curves Acceleraion a = Slope of curve Disance s = Area under curve Mahemaical Calculaions (i) Rise 6 ms a = = = ms Run 8 s s= bh = ()( 8 6 ) = 64 m (ii) s= l b = ( 0)( 6) = 30 m Con...

35 The Dublin School of Grinds Page 3 Kieran Mills & Tony Kelly Example A car saring from res acceleraes uniformly over 8 s o a velociy of 6 m s. I hen mainains a consan velociy for he nex 0 s. I finally deceleraes uniformly o res for 4 s. Draw a velociy-ime curve o represen he moion of he car. Use he graph o find (i) he acceleraion and disance ravelled by he car in he firs 8 s, (ii) he disance ravelled by he car over he nex 0 s, (iii) he deceleraion and disance ravelled by he car over he las 4 s, (iv) he average velociy of he car for is enire journey. Soluion - v (m s ) a = m s - Rise = 6 m s - Heigh h = 6 a = -4 m s - 64 m 30 m 3 m (s) Run = 4 s Base b = 4 Area of a riangle = bh Velociy Time Curves Acceleraion a = Slope of curve Disance s = Area under curve Mahemaical Calculaions (i) Rise 6 ms a = = = ms Run 8 s s= bh = ()( 8 6 ) = 64 m (ii) s= l b = ( 0)( 6) = 30 m Rise 6 ms (iii) a = = = 4 ms Run 4 s s= bh = ( 4 )( 6 ) = 3 m Con...

36 The Dublin School of Grinds Page 33 Kieran Mills & Tony Kelly Example A car saring from res acceleraes uniformly over 8 s o a velociy of 6 m s. I hen mainains a consan velociy for he nex 0 s. I finally deceleraes uniformly o res for 4 s. Draw a velociy-ime curve o represen he moion of he car. Use he graph o find (i) he acceleraion and disance ravelled by he car in he firs 8 s, (ii) he disance ravelled by he car over he nex 0 s, (iii) he deceleraion and disance ravelled by he car over he las 4 s, (iv) he average velociy of he car for is enire journey. Soluion - v (m s ) a = m s m + 30 m + 3 m = 46 m a = -4 m s - (s) Mahemaical Calculaions (iv) Average Velociy = Toal Disance Toal Time 46 m Average velociy = = 3 ms 3 s Con...

37 The Dublin School of Grinds Page 34 Kieran Mills & Tony Kelly Example A car saring from res acceleraes uniformly over 8 s o a velociy of 6 m s. I hen mainains a consan velociy for he nex 0 s. I finally deceleraes uniformly o res for 4 s. Draw a velociy-ime curve o represen he moion of he car. Use he graph o find (i) he acceleraion and disance ravelled by he car in he firs 8 s, (ii) he disance ravelled by he car over he nex 0 s, (iii) he deceleraion and disance ravelled by he car over he las 4 s, (iv) he average velociy of he car for is enire journey. Soluion - v (m s ) a = m s m 3 a = -4 m s - (s) Finding he area under he curve in one go: A rapezium is a four sided shape where wo of he sides are parallel. The area of a rapezium is half he sum of he parallel sides by he perpendicular disance beween hem. Area = ( x + y) h Mahemaical Calculaions s = ( 0 + 3)( 6) = ( 5)( 6) = ( 5)() 8 = 46 m

38 The Dublin School of Grinds Page 35 Kieran Mills & Tony Kelly Example A car ravels from A o B. I sars from res a A and acceleraes a m s unil i reaches a speed of 30 m s. I hen ravels a his speed for 600 m and hen deceleraes a.5 m s o come o res a B. Find (i) he oal ime for he journey, (ii) he disance from A o B, (iii) he average speed for he journey. Soluion Toal ime T = 5 s + 0 s + s = 47 s Velociy Time Curves Acceleraion a = Slope of curve Disance s = Area under curve Mahemaical Calculaions V 30 (i) I : a = = 30 = = 5 s s s = 600 m v = V = 30 ms =? s 600 II :V = 30 = 600 = = 0 s 30 V 30 III : a = 5. = = = 5. s Con...

39 . 4 ms The Dublin School of Grinds Page 36 Kieran Mills & Tony Kelly Example A car ravels from A o B. I sars from res a A and acceleraes a m s unil i reaches a speed of 30 m s. I hen ravels a his speed for 600 m and hen deceleraes a.5 m s o come o res a B. Find (i) he oal ime for he journey, (ii) he disance from A o B, (iii) he average speed for he journey. Soluion Toal ime T = 5 s + 0 s + s = 47 s Mahemaical Calculaions (ii) Area = ( x + y) h Average Velociy = S = ( ) 30 = 005 m Toal Disance Toal Time 005 m (iii) Average velociy = = 47 s

40 The Dublin School of Grinds Page 37 Kieran Mills & Tony Kelly Example 3 A paricle P wih speed 40 m s begins o decelerae uniformly a a cerain insan while anoher paricle Q sars from res 6 s laer and acceleraes uniformly. When he second paricle Q has ravelled 5 m, boh paricles have a speed of 5 m s. (i) Show he moion of boh on he same speed-ime curve. (ii) How many seconds afer he commencemen of deceleraion does he firs paricle P come o res? Soluion Velociy Time Curves Acceleraion a = Slope of curve Disance s = Area under curve Mahemaical Calculaions (ii) Paricle Q: s= bh 5 = ( 5) 5 = = 0 s s = 5 m h = 5 ms b=

41 The Dublin School of Grinds Page 38 Kieran Mills & Tony Kelly Example 3 A paricle P wih speed 40 m s begins o decelerae uniformly a a cerain insan while anoher paricle Q sars from res 6 s laer and acceleraes uniformly. When he second paricle Q has ravelled 5 m, boh paricles have a speed of 5 m s. (i) Show he moion of boh on he same speed-ime curve. (ii) How many seconds afer he commencemen of deceleraion does he firs paricle P come o res? Soluion Velociy Time Curves Acceleraion a = Slope of curve Disance s = Area under curve Mahemaical Calculaions (ii) Paricle P: Rise 5 a = = = 78. ms Run 6 u = 40 ms a = 78. ms v = 0 ms =? v= u+ a 0 = 40 + ( 78. ) 78. = = = s

42 Exercise 5. Velociy Time Curves. A car is ravelling a 7 km h when he brakes are applied producing a reardaion of 4 m s. How long does i ake o sop?. An elecric rain sars from a saion and reaches a speed of 4 m s in 5 s wih uniform acceleraion. Skech he velociy-ime graph, and find how far i has gone by he ime i reaches his speed. 3. An aircraf can ake off when i reaches a speed of 80 km h. If i aains his speed in 30 s wih uniform acceleraion wha disance does i require for aking off? 4. An express rain is ravelling a 44 km h when is brakes are applied. If hese produce a reardaion of m s how long will i ake o sop and wha disance will i cover in doing so? 5. A rain sars from res and aains a speed of 50 km h in 4 minues wih uniform acceleraion. I runs a ha speed for 5 minues and hen slows down uniformly o res in minues. Draw he velociy-ime graph and find he oal disance ravelled. 6. Find from he velociy-ime graph shown (i) he acceleraion during he firs 4 s, (ii) he reardaion during he las s, (iii) he oal disance ravelled. v (m/s) (s) 7. A cyclis rides along a sraigh road from A o B. He sars from res a A and acceleraes uniformly o reach a speed of 0 m s in 8 s. He mainains his speed for 30 s and hen uniformly deceleraes o res a B. If he oal ime is 48 s, draw a velociy-ime curve and from i find (i) he acceleraion, (ii) he deceleraion, (iii) he oal disance ravelled. 8. A car ravels from A o B. I sars from res a A and acceleraes a.5 m s unil i reaches a speed of 30 m s. I hen ravels a his speed for km and hen deceleraes a m s o come o res a B. Find (i) he oal ime for he journey, (ii) he disance from A o B, (iii) he average speed for he journey. 9. A and B are wo poins on a sraigh road. A car ravelling along he road passes A when = 0 and mainains a consan speed unil = 0 s, and in his ime covers four-fifhs of he disance from A o B. The car hen deceleraes uniformly o res a B. Draw a velociy-ime curve and find he ime from A o B. The Dublin School of Grinds Page 39 Kieran Mills & Tony Kelly

43 0. A ram ravels along a sraigh rack and sars from res. I acceleraes uniformly for 0 s and during his ime i ravels 60 m. I mainains a consan speed for a furher 50 s and deceleraes o res in 8 s. Calculae (i) he acceleraion, (ii) he deceleraion, (iii) he oal ime, (iv) he oal disance.. A rain sars from res and ravels 8 km in minues ending a res. The acceleraion is half he reardaion, boh are uniform, and here is a period when he rain runs a is maximum speed of 50 km h. Find he ime aken o reach full speed.. A 00 m spriner sars wih a speed of 6 m s - and acceleraes uniformly o 0 m s and finishes he race a his speed. If his oal ime is 0.4 s, find his uniform acceleraion and afer wha disance he is going a full speed. 3. A car akes minues o ravel beween wo ses of raffic lighs 45 m apar. I has uniform acceleraion for 30 s, hen uniform velociy, and hen uniform reardaion for he las 5 s. Find he maximum velociy and he acceleraion. 4. A rain ravels 5 km beween wo saions a an average speed of 50 km h. Is acceleraion is half he reardaion and boh are uniform. If he maximum speed is 7 km h find he acceleraion in m s. Skech he velociy-ime curve. 5. A car acceleraes a m s in boom gear,.5 m s in second gear and m s in op gear. Each gear change akes.5 s during which ime he car ravels a consan speed. If a mooris changes gear when his speeds are 3 m s and 9 m s find how long he will ake o reach 5 m s from res. 6. A rain moving in a sraigh line sars from A wih uniform acceleraion of 0. m s. Afer i has aained full speed i moves uniformly for 0 minues. I is brough o res a B by he brakes, which apply a consan reardaion of 0.8 m s for 0 s. Draw a rough velociy-ime graph and from i find he ime of he journey and he disance from A o B. 7. A rain has a maximum speed of 7 km h which i can achieve a an acceleraion of 0.5 m s. Wih is brakes fully applied he rain has a deceleraion of 0.5 m s. Wha is he shores ime ha he rain can ravel beween saions 8 km apar if i sops a boh saions? 8. A paricle wih speed 50 m s begins o decelerae uniformly a a cerain insan while anoher paricle sars from res 8 s laer and acceleraes uniformly. When he second paricle has ravelled 35 m, boh paricles have a speed of 30 m s. (i) Show he moion of boh on he same speed-ime curve. (ii) How many seconds afer he commencemen of deceleraion does he firs paricle come o res? The Dublin School of Grinds Page 40 Kieran Mills & Tony Kelly

44 9. A body sars from res a P ravelling in a sraigh line and hen comes o res a Q which is 696 m from P. The ime aken is 66 s. For he firs 0 s i has uniform acceleraion a. I hen ravels a consan speed and is finally brough o res by a uniform deceleraion b acing for 6 s. Find a and b. If he journey from res a P o res a Q had been ravelled wih no inerval of consan speed bu a acceleraion of a for a ime immediaely followed by deceleraion b for a ime, show ha he ime for he journey is 8 9s. 0. An ahlee runs 00 m in s. Saring from res he acceleraes uniformly o a speed of 0 m s and hen coninues a ha speed. Calculae he acceleraion.. A cyclis has a maximum acceleraion of m s, a maximum speed of 5 m s and a maximum deceleraion of 4 m s. If he ravels from res o res in he shores possible ime show ha he covers a disance of m. Find he ime o ravel (i) 05 m, (ii) 54 m. Answers Exercise 5. 5 s. 75 m km 4. 0 s, 400 m km 6. (i) m s (ii) 4 m s (iii) 56 m 7. (i).5 m s (ii) m s (iii) 390 m 8. (i) s (ii) 55 m (iii) 4.83 m s 4. ms s 6. 3 minues,.04 km s 8. (ii).5 s 9.. m s, m s 0..5 m s. (i) 5 8 s (ii) 9 s s 0. (i) 0.8 m s (ii) m s (iii) 78 s (iv) 04 m. 3. minues. m s, 6 m 3. m s, 0.73 m s The Dublin School of Grinds Page 4 Kieran Mills & Tony Kelly

45 The Dublin School of Grinds Page 4 Kieran Mills & Tony Kelly Secion 5: Free Fall Example A body is hrown verically up from he ground a 4 m s -. Find he maximum heigh i reaches and he ime o reach his heigh. From is highes poin find he ime for he body o hi he ground and is speed when i his he ground. Example A ball is hrown verically up a 0 m s - from a poin 3 m above he ground. Find he speed i has when i his he ground and he ime i akes he ball o hi he ground. Example 3 A ho-air balloon ravels from he ground verically up a a consan speed of m s -. Find is heigh above he ground afer 5 s. Afer 5 s a ball is dropped from he baloon. How long does i ake o reach he ground?

46 The Dublin School of Grinds Page 43 Kieran Mills & Tony Kelly Example A body is hrown verically up from he ground a 4 m s -. Find he maximum heigh i reaches and he ime o reach his heigh. From is highes poin find is speed when i his he ground and he ime for he body o hi he ground. Soluion Up is posiive Down is negaive s =? GOING UP v = 0 m s Going up: u = 4 m s - v = 0 m s - a = -9.8 m s - s =? =? u = 4 m s The acceleraion due o graviy is denoed by g. This value is 9.8 m s -. In free fall alway le a = -g = -9.8 m s -. v = u + as 0 = 4 + ( 98. ) s 9. 6s = s = = m v= u+ a 0= = = = = 43. s Conclusions: Time up = Time Down s = 0 m GOING DOWN u = 0 m s Going down: u = 0 m s - a = -9.8 m s - s = -0 m =? v =? v =? Up is posiive Down is negaive v = u + as v = 0 + ( 98. )( 0) v = 96 v = 96 = 4 ms v= u+ a 4 = = = = 43. s Velociy going up = Velociy a same poin on way down bu in he opposie direcion

47 The Dublin School of Grinds Page 44 Kieran Mills & Tony Kelly Example A ball is hrown verically up a 0 m s - from a poin 3 m above he ground. Find he speed i has when i his he ground and he ime i akes he ball o hi he ground. Soluion u = 0 m s s = 3 m v =? u = 0 m s - s = -3 m a = -9.8 m s - v =? =? The acceleraion due o graviy is denoed by g. This value is 9.8 m s -. In free fall alway le a = -g = -9.8 m s -. Up is posiive Down is negaive v = u + as v = 0 + ( 98. )( 3) v = 0 + ( 9. 8)( 3) =. 6 ms The velociy is negaive as i is moving down. v= u+ a. 6= = = = 3. s 98.

48 The Dublin School of Grinds Page 45 Kieran Mills & Tony Kelly Example 3 A ho-air balloon ravels from he ground verically up a a consan speed of m s -. Find is heigh above he ground afer 5 s. Afer 5 s a ball is dropped from he balloon. How long does i ake o reach he ground? Give your answer o one place of decimal. Soluion s =? = 5 s v = m s v = m s Ball is dropped =? u = m s s = 60 m v = s v = ms = 5 s s v = s= v = 5= 60 m Ball is dropped from balloon: u = m s - s = -60 m a = -9.8 m s - =? s= u+ a 60 = + ( 98. ) 60 = = 0 ± ( ) 449 (. )( 60) = 49 (. ) = 49. s

49 Exercise 6. Uniformly g acceleraed moion [In all problems g = 9.8 m s ]. A vase falls from a shelf 40 cm above he floor. Find he speed wih which i srikes he floor.. A sone is dropped from a poin 49 m above he ground. Find he ime for i o reach he ground. 3. A sone is hrown down a 5 m s. If is speed on hiing he ground is 9 m s from wha heigh was i hrown. How long does i ake? 4. A sone is dropped from he op of a ower and falls o he ground. If i srikes he ground a 4 m s, how high is he ower? 5. A ball is hrown verically downwards from he op of a ower wih an iniial speed of m s. If i his he ground 3 s laer find (i) he heigh of he ower, (ii) he speed wih which i his he ground. 6. A sone is hrown upwards wih a speed of m s. Find is heigh (i) s afer projecion, (ii) s afer projecion, (iii) 3 s afer projecion. 7. A ball is hrown up a 4 m s from a poin m above he ground. Find (i) he speed when i reurns o he level of projecion, (ii) he speed on he ground. 8. A ball is hrown verically up a 8 m s. Find (i) he maximum heigh, (ii) he ime o reach he maximum heigh, (iii) he velociy of reurn, (iv) he oal ime for he journey. 9. A balloon is rising a a seady speed of 3 m s. How high is i above he ground afer 0 s? A his insan a man releases a sone. Wha is he iniial velociy of he sone? How long does i ake o reach he ground? How high is he balloon above he ground when he sone srikes he ground? 0. A sone is hrown up a 49 m s from he ground. Find he imes a which he paricle is 78.4 m above he ground. Find he ime inerval for which he paricle is above 78.4 m.. A ball is hrown up a 4 m s. Find he imes a which he paricle is 9. m above he ground. The Dublin School of Grinds Page 46 Kieran Mills & Tony Kelly

50 . A ball is hrown up a 49 m s. How long does i ake o reach is maximum heigh? If an oher ball was hrown up s afer he firs one, how high is i above he ground when he firs ball has reached is maximum heigh if i has he same iniial velociy? 3. A jumper can jump m on he Earh. Wha is his ake-off speed? How high can he jump on he moon? (Acceleraion due o graviy of moon g =.6 m s ) 4. A paricle is hrown verically upwards under graviy wih a speed of 6 m s. One second laer anoher paricle is fired upwards from he same poin. Find he iniial speed of his paricle in order ha he wo paricles will collide when he firs paricle has reached is highes poin. 5. An objec falls verically pas a window m high in s. Find he heigh above he window from which he objec was dropped. 6. A sone is dropped from a balloon rising a 0 m s and reaches he ground in 8 s. How high was he balloon above he ground when he sone was dropped? 7. A body falls from he op of a ower and during he las second i falls 9 5 of he oal disance. Find he heigh of he ower. 8. A paricle falls freely from res from a poin O passing hree poins A, B and C, he disances AB and BC being equal. If he paricle akes 3 s o pass from A o B and s from B o C, calculae AB. 9. A body falls freely from res from a poin O passing hree poins A, B and C, he disances AB and BC being equal. The ime aken o go from A o B is s and from B o C is s. Find AB. 0. A paricle falls freely under graviy from res a a poin P. Afer i has fallen for s anoher paricle is projeced verically downwards from P wih speed 4.7 m s. Find he ime and disance from P a which hey collide. The Dublin School of Grinds Page 47 Kieran Mills & Tony Kelly

6th Year Applied Maths Higher Level Kieran Mills

6th Year Applied Maths Higher Level Kieran Mills 6h Year Applied Mahs Higher Level Kieran Mills Uniform Acceleraed Moion No par of his publicaion may be copied, reproduced or ransmied in any form or by any means, elecronic, mechanical, phoocopying, recording,

More information

IB Physics Kinematics Worksheet

IB Physics Kinematics Worksheet IB Physics Kinemaics Workshee Wrie full soluions and noes for muliple choice answers. Do no use a calculaor for muliple choice answers. 1. Which of he following is a correc definiion of average acceleraion?

More information

Displacement ( x) x x x

Displacement ( x) x x x Kinemaics Kinemaics is he branch of mechanics ha describes he moion of objecs wihou necessarily discussing wha causes he moion. 1-Dimensional Kinemaics (or 1- Dimensional moion) refers o moion in a sraigh

More information

KINEMATICS IN ONE DIMENSION

KINEMATICS IN ONE DIMENSION KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings move how far (disance and displacemen), how fas (speed and velociy), and how fas ha how fas changes (acceleraion). We say ha an objec

More information

Ground Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan

Ground Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan Ground Rules PC11 Fundamenals of Physics I Lecures 3 and 4 Moion in One Dimension A/Prof Tay Seng Chuan 1 Swich off your handphone and pager Swich off your lapop compuer and keep i No alking while lecure

More information

2.1: What is physics? Ch02: Motion along a straight line. 2.2: Motion. 2.3: Position, Displacement, Distance

2.1: What is physics? Ch02: Motion along a straight line. 2.2: Motion. 2.3: Position, Displacement, Distance Ch: Moion along a sraigh line Moion Posiion and Displacemen Average Velociy and Average Speed Insananeous Velociy and Speed Acceleraion Consan Acceleraion: A Special Case Anoher Look a Consan Acceleraion

More information

SOLUTIONS TO CONCEPTS CHAPTER 3

SOLUTIONS TO CONCEPTS CHAPTER 3 SOLUTIONS TO ONEPTS HPTER 3. a) Disance ravelled = 50 + 40 + 0 = 0 m b) F = F = D = 50 0 = 30 M His displacemen is D D = F DF 30 40 50m In ED an = DE/E = 30/40 = 3/4 = an (3/4) His displacemen from his

More information

Motion along a Straight Line

Motion along a Straight Line chaper 2 Moion along a Sraigh Line verage speed and average velociy (Secion 2.2) 1. Velociy versus speed Cone in he ebook: fer Eample 2. Insananeous velociy and insananeous acceleraion (Secions 2.3, 2.4)

More information

0 time. 2 Which graph represents the motion of a car that is travelling along a straight road with a uniformly increasing speed?

0 time. 2 Which graph represents the motion of a car that is travelling along a straight road with a uniformly increasing speed? 1 1 The graph relaes o he moion of a falling body. y Which is a correc descripion of he graph? y is disance and air resisance is negligible y is disance and air resisance is no negligible y is speed and

More information

Suggested Practice Problems (set #2) for the Physics Placement Test

Suggested Practice Problems (set #2) for the Physics Placement Test Deparmen of Physics College of Ars and Sciences American Universiy of Sharjah (AUS) Fall 014 Suggesed Pracice Problems (se #) for he Physics Placemen Tes This documen conains 5 suggesed problems ha are

More information

1. VELOCITY AND ACCELERATION

1. VELOCITY AND ACCELERATION 1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under

More information

a 10.0 (m/s 2 ) 5.0 Name: Date: 1. The graph below describes the motion of a fly that starts out going right V(m/s)

a 10.0 (m/s 2 ) 5.0 Name: Date: 1. The graph below describes the motion of a fly that starts out going right V(m/s) Name: Dae: Kinemaics Review (Honors. Physics) Complee he following on a separae shee of paper o be urned in on he day of he es. ALL WORK MUST BE SHOWN TO RECEIVE CREDIT. 1. The graph below describes he

More information

4.5 Constant Acceleration

4.5 Constant Acceleration 4.5 Consan Acceleraion v() v() = v 0 + a a() a a() = a v 0 Area = a (a) (b) Figure 4.8 Consan acceleraion: (a) velociy, (b) acceleraion When he x -componen of he velociy is a linear funcion (Figure 4.8(a)),

More information

02. MOTION. Questions and Answers

02. MOTION. Questions and Answers CLASS-09 02. MOTION Quesions and Answers PHYSICAL SCIENCE 1. Se moves a a consan speed in a consan direcion.. Reprase e same senence in fewer words using conceps relaed o moion. Se moves wi uniform velociy.

More information

Kinematics Vocabulary. Kinematics and One Dimensional Motion. Position. Coordinate System in One Dimension. Kinema means movement 8.

Kinematics Vocabulary. Kinematics and One Dimensional Motion. Position. Coordinate System in One Dimension. Kinema means movement 8. Kinemaics Vocabulary Kinemaics and One Dimensional Moion 8.1 WD1 Kinema means movemen Mahemaical descripion of moion Posiion Time Inerval Displacemen Velociy; absolue value: speed Acceleraion Averages

More information

Physics 101 Fall 2006: Exam #1- PROBLEM #1

Physics 101 Fall 2006: Exam #1- PROBLEM #1 Physics 101 Fall 2006: Exam #1- PROBLEM #1 1. Problem 1. (+20 ps) (a) (+10 ps) i. +5 ps graph for x of he rain vs. ime. The graph needs o be parabolic and concave upward. ii. +3 ps graph for x of he person

More information

MEI Mechanics 1 General motion. Section 1: Using calculus

MEI Mechanics 1 General motion. Section 1: Using calculus Soluions o Exercise MEI Mechanics General moion Secion : Using calculus. s 4 v a 6 4 4 When =, v 4 a 6 4 6. (i) When = 0, s = -, so he iniial displacemen = - m. s v 4 When = 0, v = so he iniial velociy

More information

In this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should

In this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should Cambridge Universiy Press 978--36-60033-7 Cambridge Inernaional AS and A Level Mahemaics: Mechanics Coursebook Excerp More Informaion Chaper The moion of projeciles In his chaper he model of free moion

More information

CHEAPEST PMT ONLINE TEST SERIES AIIMS/NEET TOPPER PREPARE QUESTIONS

CHEAPEST PMT ONLINE TEST SERIES AIIMS/NEET TOPPER PREPARE QUESTIONS CHEAPEST PMT ONLINE TEST SERIES AIIMS/NEET TOPPER PREPARE QUESTIONS For more deails see las page or conac @aimaiims.in Physics Mock Tes Paper AIIMS/NEET 07 Physics 06 Saurday Augus 0 Uni es : Moion in

More information

Solution: b All the terms must have the dimension of acceleration. We see that, indeed, each term has the units of acceleration

Solution: b All the terms must have the dimension of acceleration. We see that, indeed, each term has the units of acceleration PHYS 54 Tes Pracice Soluions Spring 8 Q: [4] Knowing ha in he ne epression a is acceleraion, v is speed, is posiion and is ime, from a dimensional v poin of view, he equaion a is a) incorrec b) correc

More information

Welcome Back to Physics 215!

Welcome Back to Physics 215! Welcome Back o Physics 215! (General Physics I) Thurs. Jan 19 h, 2017 Lecure01-2 1 Las ime: Syllabus Unis and dimensional analysis Today: Displacemen, velociy, acceleraion graphs Nex ime: More acceleraion

More information

9702/1/O/N/02. are set up a vertical distance h apart. M 1 M 2. , it is found that the ball takes time t 1. to reach M 2 ) 2

9702/1/O/N/02. are set up a vertical distance h apart. M 1 M 2. , it is found that the ball takes time t 1. to reach M 2 ) 2 PhysicsndMahsTuor.com 7 car is ravelling wih uniform acceleraion along a sraigh road. The road has marker poss every 1 m. When he car passes one pos, i has a speed of 1 m s 1 and, when i passes he nex

More information

x(m) t(sec ) Homework #2. Ph 231 Introductory Physics, Sp-03 Page 1 of 4

x(m) t(sec ) Homework #2. Ph 231 Introductory Physics, Sp-03 Page 1 of 4 Homework #2. Ph 231 Inroducory Physics, Sp-03 Page 1 of 4 2-1A. A person walks 2 miles Eas (E) in 40 minues and hen back 1 mile Wes (W) in 20 minues. Wha are her average speed and average velociy (in ha

More information

Physics 221 Fall 2008 Homework #2 Solutions Ch. 2 Due Tues, Sept 9, 2008

Physics 221 Fall 2008 Homework #2 Solutions Ch. 2 Due Tues, Sept 9, 2008 Physics 221 Fall 28 Homework #2 Soluions Ch. 2 Due Tues, Sep 9, 28 2.1 A paricle moving along he x-axis moves direcly from posiion x =. m a ime =. s o posiion x = 1. m by ime = 1. s, and hen moves direcly

More information

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x

WEEK-3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x WEEK-3 Reciaion PHYS 131 Ch. 3: FOC 1, 3, 4, 6, 14. Problems 9, 37, 41 & 71 and Ch. 4: FOC 1, 3, 5, 8. Problems 3, 5 & 16. Feb 8, 018 Ch. 3: FOC 1, 3, 4, 6, 14. 1. (a) The horizonal componen of he projecile

More information

Dynamics. Option topic: Dynamics

Dynamics. Option topic: Dynamics Dynamics 11 syllabusref Opion opic: Dynamics eferenceence In his cha chaper 11A Differeniaion and displacemen, velociy and acceleraion 11B Inerpreing graphs 11C Algebraic links beween displacemen, velociy

More information

Lecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.

Lecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still. Lecure - Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in

More information

1. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to t = T. a

1. The graph below shows the variation with time t of the acceleration a of an object from t = 0 to t = T. a Kinemaics Paper 1 1. The graph below shows he ariaion wih ime of he acceleraion a of an objec from = o = T. a T The shaded area under he graph represens change in A. displacemen. B. elociy. C. momenum.

More information

Unit 1 Test Review Physics Basics, Movement, and Vectors Chapters 1-3

Unit 1 Test Review Physics Basics, Movement, and Vectors Chapters 1-3 A.P. Physics B Uni 1 Tes Reiew Physics Basics, Moemen, and Vecors Chapers 1-3 * In sudying for your es, make sure o sudy his reiew shee along wih your quizzes and homework assignmens. Muliple Choice Reiew:

More information

Physics 20 Lesson 5 Graphical Analysis Acceleration

Physics 20 Lesson 5 Graphical Analysis Acceleration Physics 2 Lesson 5 Graphical Analysis Acceleraion I. Insananeous Velociy From our previous work wih consan speed and consan velociy, we know ha he slope of a posiion-ime graph is equal o he velociy of

More information

Of all of the intellectual hurdles which the human mind has confronted and has overcome in the last fifteen hundred years, the one which seems to me

Of all of the intellectual hurdles which the human mind has confronted and has overcome in the last fifteen hundred years, the one which seems to me Of all of he inellecual hurdles which he human mind has confroned and has overcome in he las fifeen hundred years, he one which seems o me o have been he mos amazing in characer and he mos supendous in

More information

Practicing Problem Solving and Graphing

Practicing Problem Solving and Graphing Pracicing Problem Solving and Graphing Tes 1: Jan 30, 7pm, Ming Hsieh G20 The Bes Ways To Pracice for Tes Bes If need more, ry suggesed problems from each new opic: Suden Response Examples A pas opic ha

More information

Conceptual Physics Review (Chapters 2 & 3)

Conceptual Physics Review (Chapters 2 & 3) Concepual Physics Review (Chapers 2 & 3) Soluions Sample Calculaions 1. My friend and I decide o race down a sraigh srech of road. We boh ge in our cars and sar from res. I hold he seering wheel seady,

More information

Physics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs.

Physics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs. Physics 180A Fall 2008 Tes 1-120 poins Name Provide he bes answer o he following quesions and problems. Wach your sig figs. 1) The number of meaningful digis in a number is called he number of. When numbers

More information

Physics for Scientists and Engineers I

Physics for Scientists and Engineers I Physics for Scieniss and Engineers I PHY 48, Secion 4 Dr. Beariz Roldán Cuenya Universiy of Cenral Florida, Physics Deparmen, Orlando, FL Chaper - Inroducion I. General II. Inernaional Sysem of Unis III.

More information

!!"#"$%&#'()!"#&'(*%)+,&',-)./0)1-*23)

!!#$%&#'()!#&'(*%)+,&',-)./0)1-*23) "#"$%&#'()"#&'(*%)+,&',-)./)1-*) #$%&'()*+,&',-.%,/)*+,-&1*#$)()5*6$+$%*,7&*-'-&1*(,-&*6&,7.$%$+*&%'(*8$&',-,%'-&1*(,-&*6&,79*(&,%: ;..,*&1$&$.$%&'()*1$$.,'&',-9*(&,%)?%*,('&5

More information

3.6 Derivatives as Rates of Change

3.6 Derivatives as Rates of Change 3.6 Derivaives as Raes of Change Problem 1 John is walking along a sraigh pah. His posiion a he ime >0 is given by s = f(). He sars a =0from his house (f(0) = 0) and he graph of f is given below. (a) Describe

More information

PHYSICS 149: Lecture 9

PHYSICS 149: Lecture 9 PHYSICS 149: Lecure 9 Chaper 3 3.2 Velociy and Acceleraion 3.3 Newon s Second Law of Moion 3.4 Applying Newon s Second Law 3.5 Relaive Velociy Lecure 9 Purdue Universiy, Physics 149 1 Velociy (m/s) The

More information

University Physics with Modern Physics 14th Edition Young TEST BANK

University Physics with Modern Physics 14th Edition Young TEST BANK Universi Phsics wih Modern Phsics 14h Ediion Young SOLUTIONS MANUAL Full clear download (no formaing errors) a: hps://esbankreal.com/download/universi-phsics-modern-phsics- 14h-ediion-oung-soluions-manual-/

More information

Physics Notes - Ch. 2 Motion in One Dimension

Physics Notes - Ch. 2 Motion in One Dimension Physics Noes - Ch. Moion in One Dimension I. The naure o physical quaniies: scalars and ecors A. Scalar quaniy ha describes only magniude (how much), NOT including direcion; e. mass, emperaure, ime, olume,

More information

AP Calculus BC Chapter 10 Part 1 AP Exam Problems

AP Calculus BC Chapter 10 Part 1 AP Exam Problems AP Calculus BC Chaper Par AP Eam Problems All problems are NO CALCULATOR unless oherwise indicaed Parameric Curves and Derivaives In he y plane, he graph of he parameric equaions = 5 + and y= for, is a

More information

x i v x t a dx dt t x

x i v x t a dx dt t x Physics 3A: Basic Physics I Shoup - Miderm Useful Equaions A y A sin A A A y an A y A A = A i + A y j + A z k A * B = A B cos(θ) A B = A B sin(θ) A * B = A B + A y B y + A z B z A B = (A y B z A z B y

More information

Physics for Scientists and Engineers. Chapter 2 Kinematics in One Dimension

Physics for Scientists and Engineers. Chapter 2 Kinematics in One Dimension Physics for Scieniss and Engineers Chaper Kinemaics in One Dimension Spring, 8 Ho Jung Paik Kinemaics Describes moion while ignoring he agens (forces) ha caused he moion For now, will consider moion in

More information

Best test practice: Take the past test on the class website

Best test practice: Take the past test on the class website Bes es pracice: Take he pas es on he class websie hp://communiy.wvu.edu/~miholcomb/phys11.hml I have posed he key o he WebAssign pracice es. Newon Previous Tes is Online. Forma will be idenical. You migh

More information

PHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections

PHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections PHYSICS 220 Lecure 02 Moion, Forces, and Newon s Laws Texbook Secions 2.2-2.4 Lecure 2 Purdue Universiy, Physics 220 1 Overview Las Lecure Unis Scienific Noaion Significan Figures Moion Displacemen: Δx

More information

Phys 221 Fall Chapter 2. Motion in One Dimension. 2014, 2005 A. Dzyubenko Brooks/Cole

Phys 221 Fall Chapter 2. Motion in One Dimension. 2014, 2005 A. Dzyubenko Brooks/Cole Phys 221 Fall 2014 Chaper 2 Moion in One Dimension 2014, 2005 A. Dzyubenko 2004 Brooks/Cole 1 Kinemaics Kinemaics, a par of classical mechanics: Describes moion in erms of space and ime Ignores he agen

More information

Q.1 Define work and its unit?

Q.1 Define work and its unit? CHP # 6 ORK AND ENERGY Q.1 Define work and is uni? A. ORK I can be define as when we applied a force on a body and he body covers a disance in he direcion of force, hen we say ha work is done. I is a scalar

More information

1. Kinematics I: Position and Velocity

1. Kinematics I: Position and Velocity 1. Kinemaics I: Posiion and Velociy Inroducion The purpose of his eperimen is o undersand and describe moion. We describe he moion of an objec by specifying is posiion, velociy, and acceleraion. In his

More information

Today: Falling. v, a

Today: Falling. v, a Today: Falling. v, a Did you ge my es email? If no, make sure i s no in your junk box, and add sbs0016@mix.wvu.edu o your address book! Also please email me o le me know. I will be emailing ou pracice

More information

Q2.1 This is the x t graph of the motion of a particle. Of the four points P, Q, R, and S, the velocity v x is greatest (most positive) at

Q2.1 This is the x t graph of the motion of a particle. Of the four points P, Q, R, and S, the velocity v x is greatest (most positive) at Q2.1 This is he x graph of he moion of a paricle. Of he four poins P, Q, R, and S, he velociy is greaes (mos posiive) a A. poin P. B. poin Q. C. poin R. D. poin S. E. no enough informaion in he graph o

More information

2. What is the displacement of the bug between t = 0.00 s and t = 20.0 s? A) cm B) 39.9 cm C) cm D) 16.1 cm E) +16.

2. What is the displacement of the bug between t = 0.00 s and t = 20.0 s? A) cm B) 39.9 cm C) cm D) 16.1 cm E) +16. 1. For which one of he following siuaions will he pah lengh equal he magniude of he displacemen? A) A jogger is running around a circular pah. B) A ball is rolling down an inclined plane. C) A rain ravels

More information

Equations of motion for constant acceleration

Equations of motion for constant acceleration Lecure 3 Chaper 2 Physics I 01.29.2014 Equaions of moion for consan acceleraion Course websie: hp://faculy.uml.edu/andriy_danylo/teaching/physicsi Lecure Capure: hp://echo360.uml.edu/danylo2013/physics1spring.hml

More information

Chapter 3 Kinematics in Two Dimensions

Chapter 3 Kinematics in Two Dimensions Chaper 3 KINEMATICS IN TWO DIMENSIONS PREVIEW Two-dimensional moion includes objecs which are moing in wo direcions a he same ime, such as a projecile, which has boh horizonal and erical moion. These wo

More information

Section A: Forces and Motion

Section A: Forces and Motion I is very useful o be able o make predicions abou he way moving objecs behave. In his chaper you will learn abou some equaions of moion ha can be used o calculae he speed and acceleraion of objecs, and

More information

Variable acceleration, Mixed Exercise 11

Variable acceleration, Mixed Exercise 11 Variable acceleraion, Mixed Exercise 11 1 a v 1 P is a res when v 0. 0 1 b s 0 0 v d (1 ) 1 0 1 0 7. The disance ravelled by P is 7. m. 1 a v 6+ a d v 6 + When, a 6+ 0 The acceleraion of P when is 0 m

More information

RELATIVE MOTION. Contents. Theory 01. Exercise Exercise Exercise Exercise Answer Key 13.

RELATIVE MOTION. Contents. Theory 01. Exercise Exercise Exercise Exercise Answer Key 13. RELAIVE MOION Conens opic Page No. heory 01 Exercise - 1 0-07 Exercise - 08-09 Exercise - 3 09-11 Exercise - 4 1 Answer Key 13 Syllabus Relaive Velociy Name : Conac No. ARRIDE LEARNING ONLINE E-LEARNING

More information

CHAPTER 2. Answer to Checkpoint Questions

CHAPTER 2. Answer to Checkpoint Questions CHAPTER MOTION ALONG A STRAIGHT LINE CHAPTER Answer o Checkpoin Quesions. (b) and (c). zero 3. (a) () and (4); (b) () and (3); (c) (3) 4. (a) plus; (b) minus; (c) minus; (d) plus 5. () and (4) 6. (a) plus;

More information

MOMENTUM CONSERVATION LAW

MOMENTUM CONSERVATION LAW 1 AAST/AEDT AP PHYSICS B: Impulse and Momenum Le us run an experimen: The ball is moving wih a velociy of V o and a force of F is applied on i for he ime inerval of. As he resul he ball s velociy changes

More information

Parametrics and Vectors (BC Only)

Parametrics and Vectors (BC Only) Paramerics and Vecors (BC Only) The following relaionships should be learned and memorized. The paricle s posiion vecor is r() x(), y(). The velociy vecor is v(),. The speed is he magniude of he velociy

More information

Kinematics in One Dimension

Kinematics in One Dimension Kinemaics in One Dimension PHY 7 - d-kinemaics - J. Hedberg - 7. Inroducion. Differen Types of Moion We'll look a:. Dimensionaliy in physics 3. One dimensional kinemaics 4. Paricle model. Displacemen Vecor.

More information

~v = x. ^x + ^y + ^x + ~a = vx. v = v 0 + at. ~v P=A = ~v P=B + ~v B=A. f k = k. W tot =KE. P av =W=t. W grav = mgy 1, mgy 2 = mgh =,U grav

~v = x. ^x + ^y + ^x + ~a = vx. v = v 0 + at. ~v P=A = ~v P=B + ~v B=A. f k = k. W tot =KE. P av =W=t. W grav = mgy 1, mgy 2 = mgh =,U grav PHYSICS 5A FALL 2001 FINAL EXAM v = x a = v x = 1 2 a2 + v 0 + x 0 v 2 = v 2 0 +2a(x, x 0) a = v2 r ~v = x ~a = vx v = v 0 + a y z ^x + ^y + ^z ^x + vy x, x 0 = 1 2 (v 0 + v) ~v P=A = ~v P=B + ~v B=A ^y

More information

Physics 218 Exam 1. with Solutions Fall 2010, Sections Part 1 (15) Part 2 (20) Part 3 (20) Part 4 (20) Bonus (5)

Physics 218 Exam 1. with Solutions Fall 2010, Sections Part 1 (15) Part 2 (20) Part 3 (20) Part 4 (20) Bonus (5) Physics 18 Exam 1 wih Soluions Fall 1, Secions 51-54 Fill ou he informaion below bu o no open he exam unil insruce o o so! Name Signaure Suen ID E-mail Secion # ules of he exam: 1. You have he full class

More information

2002 November 14 Exam III Physics 191

2002 November 14 Exam III Physics 191 November 4 Exam III Physics 9 Physical onsans: Earh s free-fall acceleraion = g = 9.8 m/s ircle he leer of he single bes answer. quesion is worh poin Each 3. Four differen objecs wih masses: m = kg, m

More information

Physics 3A: Basic Physics I Shoup Sample Midterm. Useful Equations. x f. x i v x. a x. x i. v xi v xf. 2a x f x i. y f. a r.

Physics 3A: Basic Physics I Shoup Sample Midterm. Useful Equations. x f. x i v x. a x. x i. v xi v xf. 2a x f x i. y f. a r. Physics 3A: Basic Physics I Shoup Sample Miderm Useful Equaions A y Asin A A x A y an A y A x A = A x i + A y j + A z k A * B = A B cos(θ) A x B = A B sin(θ) A * B = A x B x + A y B y + A z B z A x B =

More information

and v y . The changes occur, respectively, because of the acceleration components a x and a y

and v y . The changes occur, respectively, because of the acceleration components a x and a y Week 3 Reciaion: Chaper3 : Problems: 1, 16, 9, 37, 41, 71. 1. A spacecraf is raveling wih a veloci of v0 = 5480 m/s along he + direcion. Two engines are urned on for a ime of 84 s. One engine gives he

More information

One-Dimensional Kinematics

One-Dimensional Kinematics One-Dimensional Kinemaics One dimensional kinemaics refers o moion along a sraigh line. Een hough we lie in a 3-dimension world, moion can ofen be absraced o a single dimension. We can also describe moion

More information

Constant Acceleration

Constant Acceleration Objecive Consan Acceleraion To deermine he acceleraion of objecs moving along a sraigh line wih consan acceleraion. Inroducion The posiion y of a paricle moving along a sraigh line wih a consan acceleraion

More information

SPH3U: Projectiles. Recorder: Manager: Speaker:

SPH3U: Projectiles. Recorder: Manager: Speaker: SPH3U: Projeciles Now i s ime o use our new skills o analyze he moion of a golf ball ha was ossed hrough he air. Le s find ou wha is special abou he moion of a projecile. Recorder: Manager: Speaker: 0

More information

Lecture 4 Kinetics of a particle Part 3: Impulse and Momentum

Lecture 4 Kinetics of a particle Part 3: Impulse and Momentum MEE Engineering Mechanics II Lecure 4 Lecure 4 Kineics of a paricle Par 3: Impulse and Momenum Linear impulse and momenum Saring from he equaion of moion for a paricle of mass m which is subjeced o an

More information

Lab #2: Kinematics in 1-Dimension

Lab #2: Kinematics in 1-Dimension Reading Assignmen: Chaper 2, Secions 2-1 hrough 2-8 Lab #2: Kinemaics in 1-Dimension Inroducion: The sudy of moion is broken ino wo main areas of sudy kinemaics and dynamics. Kinemaics is he descripion

More information

Position, Velocity, and Acceleration

Position, Velocity, and Acceleration rev 06/2017 Posiion, Velociy, and Acceleraion Equipmen Qy Equipmen Par Number 1 Dynamic Track ME-9493 1 Car ME-9454 1 Fan Accessory ME-9491 1 Moion Sensor II CI-6742A 1 Track Barrier Purpose The purpose

More information

15. Vector Valued Functions

15. Vector Valued Functions 1. Vecor Valued Funcions Up o his poin, we have presened vecors wih consan componens, for example, 1, and,,4. However, we can allow he componens of a vecor o be funcions of a common variable. For example,

More information

d = ½(v o + v f) t distance = ½ (initial velocity + final velocity) time

d = ½(v o + v f) t distance = ½ (initial velocity + final velocity) time BULLSEYE Lab Name: ANSWER KEY Dae: Pre-AP Physics Lab Projecile Moion Weigh = 1 DIRECTIONS: Follow he insrucions below, build he ramp, ake your measuremens, and use your measuremens o make he calculaions

More information

Kinematics Motion in 1 Dimension and Graphs

Kinematics Motion in 1 Dimension and Graphs Kinemaics Moion in 1 Dimension and Graphs Lana Sheridan De Anza College Sep 27, 2017 Las ime moion in 1-dimension some kinemaic quaniies graphs Overview velociy and speed acceleraion more graphs Kinemaics

More information

Farr High School NATIONAL 5 PHYSICS. Unit 3 Dynamics and Space. Exam Questions

Farr High School NATIONAL 5 PHYSICS. Unit 3 Dynamics and Space. Exam Questions Farr High School NATIONAL 5 PHYSICS Uni Dynamics and Space Exam Quesions VELOCITY AND DISPLACEMENT D B D 4 E 5 B 6 E 7 E 8 C VELOCITY TIME GRAPHS (a) I is acceleraing Speeding up (NOT going down he flume

More information

Today: Graphing. Note: I hope this joke will be funnier (or at least make you roll your eyes and say ugh ) after class. v (miles per hour ) Time

Today: Graphing. Note: I hope this joke will be funnier (or at least make you roll your eyes and say ugh ) after class. v (miles per hour ) Time +v Today: Graphing v (miles per hour ) 9 8 7 6 5 4 - - Time Noe: I hope his joke will be funnier (or a leas make you roll your eyes and say ugh ) afer class. Do yourself a favor! Prof Sarah s fail-safe

More information

Physics 5A Review 1. Eric Reichwein Department of Physics University of California, Santa Cruz. October 31, 2012

Physics 5A Review 1. Eric Reichwein Department of Physics University of California, Santa Cruz. October 31, 2012 Physics 5A Review 1 Eric Reichwein Deparmen of Physics Universiy of California, Sana Cruz Ocober 31, 2012 Conens 1 Error, Sig Figs, and Dimensional Analysis 1 2 Vecor Review 2 2.1 Adding/Subracing Vecors.............................

More information

Physics for Scientists & Engineers 2

Physics for Scientists & Engineers 2 Direc Curren Physics for Scieniss & Engineers 2 Spring Semeser 2005 Lecure 16 This week we will sudy charges in moion Elecric charge moving from one region o anoher is called elecric curren Curren is all

More information

Reading from Young & Freedman: For this topic, read sections 25.4 & 25.5, the introduction to chapter 26 and sections 26.1 to 26.2 & 26.4.

Reading from Young & Freedman: For this topic, read sections 25.4 & 25.5, the introduction to chapter 26 and sections 26.1 to 26.2 & 26.4. PHY1 Elecriciy Topic 7 (Lecures 1 & 11) Elecric Circuis n his opic, we will cover: 1) Elecromoive Force (EMF) ) Series and parallel resisor combinaions 3) Kirchhoff s rules for circuis 4) Time dependence

More information

Speed and Velocity. Overview. Velocity & Speed. Speed & Velocity. Instantaneous Velocity. Instantaneous and Average

Speed and Velocity. Overview. Velocity & Speed. Speed & Velocity. Instantaneous Velocity. Instantaneous and Average Overview Kinemaics: Descripion of Moion Posiion and displacemen velociy»insananeous acceleraion»insananeous Speed Velociy Speed and Velociy Speed & Velociy Velociy & Speed A physics eacher walks 4 meers

More information

UCLA: Math 3B Problem set 3 (solutions) Fall, 2018

UCLA: Math 3B Problem set 3 (solutions) Fall, 2018 UCLA: Mah 3B Problem se 3 (soluions) Fall, 28 This problem se concenraes on pracice wih aniderivaives. You will ge los of pracice finding simple aniderivaives as well as finding aniderivaives graphically

More information

Chapter 2. Motion along a straight line

Chapter 2. Motion along a straight line Chaper Moion along a sraigh line Kinemaics & Dynamics Kinemaics: Descripion of Moion wihou regard o is cause. Dynamics: Sudy of principles ha relae moion o is cause. Basic physical ariables in kinemaics

More information

t A. 3. Which vector has the largest component in the y-direction, as defined by the axes to the right?

t A. 3. Which vector has the largest component in the y-direction, as defined by the axes to the right? Ke Name Insrucor Phsics 1210 Exam 1 Sepember 26, 2013 Please wrie direcl on he exam and aach oher shees of work if necessar. Calculaors are allowed. No noes or books ma be used. Muliple-choice problems

More information

CLASS XI SET A PHYSICS. 1. If and Let. The correct order of % error in. (a) (b) x = y > z (c) x < z < y (d) x > z < y

CLASS XI SET A PHYSICS. 1. If and Let. The correct order of % error in. (a) (b) x = y > z (c) x < z < y (d) x > z < y PHYSICS 1. If and Le. The correc order of % error in (a) (b) x = y > z x < z < y x > z < y. A hollow verical cylinder of radius r and heigh h has a smooh inernal surface. A small paricle is placed in conac

More information

Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS FINAL EXAMINATION June 2010.

Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS FINAL EXAMINATION June 2010. Name: Teacher: DO NOT OPEN THE EXAMINATION PAPER UNTIL YOU ARE TOLD BY THE SUPERVISOR TO BEGIN PHYSICS 224 FINAL EXAMINATION June 21 Value: 1% General Insrucions This examinaion consiss of wo pars. Boh

More information

t = x v = 18.4m 44.4m/s =0.414 s.

t = x v = 18.4m 44.4m/s =0.414 s. 1 Assuming he horizonal velociy of he ball is consan, he horizonal displacemen is x = v where x is he horizonal disance raveled, is he ime, and v is he (horizonal) velociy Convering v o meers per second,

More information

Topic 1: Linear motion and forces

Topic 1: Linear motion and forces TOPIC 1 Topic 1: Linear moion and forces 1.1 Moion under consan acceleraion Science undersanding 1. Linear moion wih consan elociy is described in erms of relaionships beween measureable scalar and ecor

More information

Physics 30: Chapter 2 Exam Momentum & Impulse

Physics 30: Chapter 2 Exam Momentum & Impulse Physics 30: Chaper 2 Exam Momenum & Impulse Name: Dae: Mark: /29 Numeric Response. Place your answers o he numeric response quesions, wih unis, in he blanks a he side of he page. (1 mark each) 1. A golfer

More information

2001 November 15 Exam III Physics 191

2001 November 15 Exam III Physics 191 1 November 15 Eam III Physics 191 Physical Consans: Earh s free-fall acceleraion = g = 9.8 m/s 2 Circle he leer of he single bes answer. quesion is worh 1 poin Each 3. Four differen objecs wih masses:

More information

SPH3U1 Lesson 03 Kinematics

SPH3U1 Lesson 03 Kinematics SPH3U1 Lesson 03 Kinemaics GRAPHICAL ANALYSIS LEARNING GOALS Sudens will Learn how o read values, find slopes and calculae areas on graphs. Learn wha hese values mean on boh posiion-ime and velociy-ime

More information

72 Calculus and Structures

72 Calculus and Structures 72 Calculus and Srucures CHAPTER 5 DISTANCE AND ACCUMULATED CHANGE Calculus and Srucures 73 Copyrigh Chaper 5 DISTANCE AND ACCUMULATED CHANGE 5. DISTANCE a. Consan velociy Le s ake anoher look a Mary s

More information

Unit 1 - Descriptive Models for Linear Motion

Unit 1 - Descriptive Models for Linear Motion Uni 1 - Descripive Models for Linear Moion A workbook and noebook for sudens aking Physics wih Mr. Lonon. Version 3. 212 1 Aciviy 1 - Umm, which way did he go? Designing an invesigaion for our buggy. You

More information

PHYS 100: Lecture 2. Motion at Constant Acceleration. Relative Motion: Reference Frames. x x = v t + a t. x = vdt. v = adt. x Tortoise.

PHYS 100: Lecture 2. Motion at Constant Acceleration. Relative Motion: Reference Frames. x x = v t + a t. x = vdt. v = adt. x Tortoise. a PHYS 100: Lecure 2 Moion a Consan Acceleraion a 0 0 Area a 0 a 0 v ad v v0 a0 v 0 x vd 0 A(1/2)( v) Area v 0 v v-v 0 v 0 x x v + a 1 0 0 2 0 2 Relaive Moion: Reference Frames x d Achilles Toroise x Toroise

More information

AP Calculus BC 2004 Free-Response Questions Form B

AP Calculus BC 2004 Free-Response Questions Form B AP Calculus BC 200 Free-Response Quesions Form B The maerials included in hese files are inended for noncommercial use by AP eachers for course and exam preparaion; permission for any oher use mus be sough

More information

Decimal moved after first digit = 4.6 x Decimal moves five places left SCIENTIFIC > POSITIONAL. a) g) 5.31 x b) 0.

Decimal moved after first digit = 4.6 x Decimal moves five places left SCIENTIFIC > POSITIONAL. a) g) 5.31 x b) 0. PHYSICS 20 UNIT 1 SCIENCE MATH WORKSHEET NAME: A. Sandard Noaion Very large and very small numbers are easily wrien using scienific (or sandard) noaion, raher han decimal (or posiional) noaion. Sandard

More information

AP CALCULUS AB/CALCULUS BC 2016 SCORING GUIDELINES. Question 1. 1 : estimate = = 120 liters/hr

AP CALCULUS AB/CALCULUS BC 2016 SCORING GUIDELINES. Question 1. 1 : estimate = = 120 liters/hr AP CALCULUS AB/CALCULUS BC 16 SCORING GUIDELINES Quesion 1 (hours) R ( ) (liers / hour) 1 3 6 8 134 119 95 74 7 Waer is pumped ino a ank a a rae modeled by W( ) = e liers per hour for 8, where is measured

More information

AP CALCULUS BC 2016 SCORING GUIDELINES

AP CALCULUS BC 2016 SCORING GUIDELINES 6 SCORING GUIDELINES Quesion A ime, he posiion of a paricle moving in he xy-plane is given by he parameric funcions ( x ( ), y ( )), where = + sin ( ). The graph of y, consising of hree line segmens, is

More information

Math 10C: Relations and Functions PRACTICE EXAM

Math 10C: Relations and Functions PRACTICE EXAM Mah C: Relaions and Funcions PRACTICE EXAM. Cailin rides her bike o school every day. The able of values shows her disance from home as ime passes. An equaion ha describes he daa is: ime (minues) disance

More information

k 1 k 2 x (1) x 2 = k 1 x 1 = k 2 k 1 +k 2 x (2) x k series x (3) k 2 x 2 = k 1 k 2 = k 1+k 2 = 1 k k 2 k series

k 1 k 2 x (1) x 2 = k 1 x 1 = k 2 k 1 +k 2 x (2) x k series x (3) k 2 x 2 = k 1 k 2 = k 1+k 2 = 1 k k 2 k series Final Review A Puzzle... Consider wo massless springs wih spring consans k 1 and k and he same equilibrium lengh. 1. If hese springs ac on a mass m in parallel, hey would be equivalen o a single spring

More information