KINEMATICS IN ONE DIMENSION


 Marjorie King
 4 years ago
 Views:
Transcription
1 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 moving in a sraigh line is moving in one dimension, and an objec which is moving in a curved pah (like a projecile) is moving in wo dimensions. We relae all hese quaniies wih a se of equaions called he kinemaic equaions. QUICK REFERENCE Imporan Terms acceleraion he rae of change in velociy acceleraion due o graviy he acceleraion of a freely falling objec in he absence of air resisance, which near he earh s surface is approximaely 1 m/s. acceleraionime graph plo of he acceleraion of an objec as a funcion of ime average acceleraion he acceleraion of an objec measured over a ime inerval average velociy he velociy of an objec measured over a ime inerval; he displacemen of an objec divided by he change in ime during he moion consan (or uniform) acceleraion acceleraion which does no change during a ime inerval consan (or uniform) velociy velociy which does no change during a ime inerval displacemen change in posiion in a paricular direcion (vecor) disance he lengh moved beween wo poins (scalar) free fall moion under he influence of graviy iniial velociy he velociy a which an objec sars a he beginning of a ime inerval 19
2 insananeous he value of a quaniy a a paricular insan of ime, such as insananeous posiion, velociy, or acceleraion kinemaics he sudy of how moion occurs, including disance, displacemen, speed, velociy, acceleraion, and ime. posiionime graph he graph of he moion of an objec ha shows how is posiion varies wih ime speed he raio of disance o ime velociy raio of he displacemen of an objec o a ime inerval velociyime graph plo of he velociy of an objec as a funcion of ime, he slope of which is acceleraion, and he area under which is displacemen Equaions and Symbols v vo a = v = v + a 1 Δx = ( vo + v) 1 Δx = vo + a v o = v o + aδx where Δx = displacemen (final posiion iniial posiion) v = velociy or speed a any ime v o = iniial velociy or speed = ime a = acceleraion
3 DISCUSSION OF SELECTED SECTIONS Displacemen Disance d can be defined as oal lengh moved. If you run around a circular rack, you have covered a disance equal o he circumference of he rack. Disance is a scalar, which means i has no direcion associaed wih i. Displacemen Δx, however, is a vecor. Displacemen is defined as he sraighline disance beween wo poins, and is a vecor which poins from an objec s iniial posiion x o oward is final posiion x f. In our previous example, if you run around a circular rack and end up a he same place you sared, your displacemen is zero, since here is no disance beween your saring poin and your ending poin. Displacemen is ofen wrien in is scalar form as simply Δx or x. Speed and Velociy Average speed is defined as he amoun of disance a moving objec covers divided by he amoun of ime i akes o cover ha disance: average speed = v = disance elapsed ime d = where v sands for speed, d is for disance, and is ime. Average velociy is defined a lile differenly han average speed. While average speed is he oal change in disance divided by he oal change in ime, average velociy is he displacemen divided by he change in ime. Since velociy is a vecor, we mus define i in erms of anoher vecor, displacemen. Ofenimes average speed and average velociy are inerchangeable for he purposes of he AP Physics B exam. Speed is he magniude of velociy, ha is, speed is a scalar and velociy is a vecor. For example, if you are driving wes a 5 miles per hour, we say ha your speed is 5 mph, and your velociy is 5 mph wes. We will use he leer v for boh speed and velociy in our calculaions, and will ake he direcion of velociy ino accoun when necessary. Acceleraion Acceleraion ells us how fas velociy is changing. For example, if you sar from res on he goal line of a fooball field, and begin walking up o a speed of 1 m/s for he firs second, hen up o m/s, for he second second, hen up o 3 m/s for he hird second, you are speeding up wih an average acceleraion of 1 m/s for each second you are walking. We wrie Δv 1m / s m a = = = 1m / s / s = 1 Δ 1s s In oher words, you are changing your speed by 1 m/s for each second you walk. If you sar wih a high velociy and slow down, you are sill acceleraing, bu your acceleraion would be considered negaive, compared o he posiive acceleraion discussed above. 1
4 Usually, he change in speed Δv is calculaed by he final speed v f minus he iniial speed v o. The iniial and final speeds are called insananeous speeds, since hey each occur a a paricular insan in ime and are no average speeds. Applicaions of he Equaions of Kinemaics for Consan Acceleraion Kinemaics is he sudy of he relaionships beween disance and displacemen, speed and velociy, acceleraion, and ime. The kinemaic equaions are he equaions of moion which relae hese quaniies o each oher. These equaions assume ha he acceleraion of an objec is uniform, ha is, consan for he ime inerval we are ineresed in. The kinemaic equaions lised below would no work for calculaing velociies and displacemens for an objec which is acceleraing erraically. Forunaely, he AP Physics B exam generally deals wih uniform acceleraion, so he kinemaic equaions lised above will be very helpful in solving problems on he es. Freely Falling Bodies An objec is in free fall if i is falling freely under he influence of graviy. Any objec, regardless of is mass, falls near he surface of he Earh wih an acceleraion of 9.8 m/s, which we will denoe wih he leer g. We will round he free fall acceleraion g o 1 m/s for he purpose of he AP Physics B exam. This free fall acceleraion assumes ha here is no air resisance o impede he moion of he falling objec, and his is a safe assumpion on he AP Physics B es unless you are old differenly for a paricular quesion on he exam. Since he free fall acceleraion is consan, we may use he kinemaic equaions o solve problems involving free fall. We simply need o replace he acceleraion a wih he specific free fall acceleraion g in each equaion. Remember, anyime a velociy and acceleraion are in opposie direcions (like when a ball is rising afer being hrown upward), you mus give one of hem a negaive sign.
5 Example 1 A girl is holding a ball as she seps ono a all elevaor on he ground floor of a building. The girl holds he ball a a heigh of 1 meer above he elevaor floor. The elevaor begins acceleraing upward from res a 3 m/s. Afer he elevaor acceleraes for 5 seconds, find (a) he speed of he elevaor (b) he heigh of he floor of he elevaor above he ground. A he end of 5 s, he girl les go of he ball from a heigh of 1 meer above he floor of he elevaor. If he elevaor coninues o accelerae upward a 3 m/s, describe he moion of he ball (c) relaive o he girl s hand, (d) relaive o he ground. (e) Deermine he ime afer he ball is released ha i will make conac wih he floor. (f) Wha is he heigh above he ground of he ball and floor when hey firs make conac? Soluion: (a) v = vo + a = + ( 3m / s )( 5s) = 15 m / s upward (b) y v 1 1 = o + a = + ( 3m / s )( 5s) = 37. 5m (c) When he girl releases he ball, boh she and he ball are moving wih a speed of 15 m/s upward. However, he girl coninues o accelerae upward a 3 m/s, bu he ball ceases o accelerae upward, and he ball s acceleraion is direced downward a g = 1 m/s, ha is, i is in free fall wih an iniial upward velociy of 15 m/s. Therefore he ball will appear o he girl o fall downward wih an acceleraion of 3 m/s ( 1 m/s ) = 13 m/s downward, and will quickly fall below her hand. (d) Someone waching he ball from he ground would simply see he ball rising upward wih an iniial velociy of 15 m/s, and would wach i rise o a maximum heigh, a which poin i would be insananeously a res (provided i doesn srike he floor of he elevaor before i reaches is maximum heigh). (e) When he ball is released, i is raveling upward wih a speed of 15 m/s, has a downward acceleraion of 13 m/s relaive o he floor, and is a a heigh y = 1 m above he floor. The ime i akes o fall o he floor is 3
6 1 y = a 1 1m = =.4 s ( 13m / s ) (f) In his ime of.4 s, he elevaor floor has moved up a disance of 1 1 Δ y = ae = ( 3m / s )(.4s) =. 4 m Thus, he ball and elevaor floor collide a a heigh above he ground of 37.5 m +.4 m = m. Graphical Analysis of Velociy and Acceleraion Le s ake some ime o review how we inerpre he moion of an objec when we are given he informaion abou i in graphical form. On he AP Physics B exam, you will need o be able o inerpre hree ypes of graphs: posiion vs.ime, velociy vs. ime, and acceleraion vs. ime. Posiion vs. ime Consider he posiion vs. ime graph below: x (m) Δx x (m) P Δx Δ Δ (s) (s) Δ x The slope of he graph on he lef is, and is herefore velociy. The curved graph on Δ he righ indicaes ha he slope is changing. The slope of he curved graph is sill velociy, even hough he velociy is changing, indicaing he objec is acceleraing. The insananeous velociy a any poin on he graph (such as poin P) can be found by drawing a angen line a he poin and finding he slope of he angen line. 4
7 Velociy vs. ime Consider he velociy vs. ime graph below: v (m/s) Δv v (m/s) Δ v As shown in he figure on he lef, he slope of a velociy vs. ime graph is, and is Δ herefore acceleraion. As shown on he figure on he righ, he area under a velociy vs. m ime graph would have unis of ( s) = m, and is herefore displacemen. s Acceleraion vs. ime Δ (s) Area Since he AP Physics B exam generally deals wih consan acceleraion, any graph of acceleraion vs. ime on he exam would likely be a sraigh horizonal line: (s) a (m/s ) +5 m/s a (m/s ) (s) 5 m/s (s) This graph on he lef ells us ha he acceleraion of his objec is posiive. If he objec were acceleraing negaively, he horizonal line would be below he ime axis, as shown in he graph on he righ. 5
8 Example Consider he posiion vs. ime graph below represening he moion of a car. Assume ha all acceleraions of he car are consan. G H I J x(m) C D E F B K (s) A On he axes below, skech he velociy vs. ime and acceleraion vs. ime graphs for his car. v(m/s) (s) a(m/s ) (s) 6
9 Soluion: The car sars ou a a disance behind our reference poin of zero, indicaed on he graph as a negaive displacemen. The velociy (slope) of he car is iniially posiive and consan from poins A o C, wih he car crossing he reference poin a B. Beween poins C and D, he car goes from a high posiive velociy (slope) o a low velociy, evenually coming o res (v = ) a poin D. A poin E he car acceleraes posiively from res up o a posiive consan velociy from poins F o G. Then he velociy (slope) decreases from poins G o H, indicaing he car is slowing down. I is beween hese wo poins ha he car s velociy is posiive, bu is acceleraion is negaive, since he car s velociy and acceleraion are in opposie direcions. The car once again comes o res a poin H, and hen begins gaining a negaive velociy (moving backward) from res a poin I, increasing is speed negaively o a consan negaive velociy beween poins J and K. A K, he car has reurned o is original saring posiion. The velociy vs. ime graph for his car would look like his: v(m/s) B C F G A D E H I (s) J K The acceleraion vs. ime graph for his car would look like his: a(m/s ) E F A B C D G H I J K (s) 7
10 REVIEW QUESTIONS For each of he muliple choice quesions below, choose he bes answer. Unless oherwise noed, use g = 1 m/s and neglec air resisance. 1. Which of he following saemens is rue? (A) Displacemen is a scalar and disance is a vecor. (B) Displacemen is a vecor and disance is a scalar. (C) Boh displacemen and disance are vecors. (D) Neiher displacemen nor disance are vecors. (E) Displacemen and disance are always equal.. Which of he following is he bes saemen for a velociy? (A) 6 miles per hour (B) 3 meers per second (C) 3 km a 45 norh of eas (D) 4 km/hr (E) 5 km/hr souhwes 3. A jogger runs 4 km in.4 hr, hen 8 km in.8 hr. Wha is he average speed of he jogger? (A) 1 km/hr (B) 3 km/hr (C) 1 km/hr (D).1 km/hr (E) 1 km/hr 5. A bus saring from a speed of +4 m/s slows o 6 m/s in a ime of 3 s. The average acceleraion of he bus is (A) m/s (B) 4 m/s (C) 6 m/s (D) m/s (E) 6 m/s 6. A rain acceleraes from res wih an acceleraion of 4 m/s for a ime of s. Wha is he rain s speed a he end of s? (A).5 m/s (B) 4 m/s (C).5 m/s (D).8 m/s (E) 8 m/s 7. A fooball player sars from res 1 meers from he goal line and acceleraes away from he goal line a 5 m/s. How far from he goal line is he player afer 4 s? (A) 6 m (B) 3 m (C) 4 m (D) 5 m (E) 6 m 4. A moorcycle sars from res and acceleraes o a speed of m/s in a ime of 8 s. Wha is he moorcycle s average acceleraion? (A) 16 m/s (B) 8 m/s (C) 8 m/s (D).5 m/s (E).4 m/s 8
11 8. A ball is dropped from res. Wha is he acceleraion of he ball immediaely afer i is dropped? (A) zero (B) 5 m/s (C) 1 m/s (D) m/s (E) 3 m/s Quesions 9 11: A ball is hrown sraigh upward wih a speed of +1 m/s. 1. Which wo of he following pairs of graphs are equivalen? (A) x v 9. Wha is he ball s acceleraion jus afer i is hrown? (A) zero (B) 1 m/s upward (C) 1 m/s downward (D) 1 m/s upward (E) 1 m/s downward (B) x v 1. How much ime does i ake for he ball o rise o is maximum heigh? (A) 4 s (B) 1 s (C) 1 s (D) s (E) 1. s (C) (D) x x v v 11. Wha is he approximae maximum heigh he ball reaches? (A) 4 m (B) 17 m (C) 1 m (D) 7 m (E) 5 m (E) x v 9
12 Quesions 13 14: Consider he velociy vs ime graph below: 13. A which ime(s) is he objec a res? (A) zero (B) 1 s (C) 3 s o 4 s (D) 4 s only (E) 8 s 14. During which inerval is he speed of he objec decreasing? (A) o 1 s (B) 1 s o 3 s (C) 3 s o 4 s (D) 4 s o 8 s (E) he speed of he objec is never decreasing in his graph 3
13 Free Response Quesion Direcions: Show all work in working he following quesion. The quesion is worh 15 poins, and he suggesed ime for answering he quesion is abou 15 minues. The pars wihin a quesion may no have equal weigh. 1. (15 poins) A car on a long horizonal rack can move wih negligible fricion o he lef or o he righ. During he ime inervals when he car is acceleraing, he acceleraion is consan. The acceleraion during oher ime inervals is also consan, bu may have a differen value. Daa is aken on he moion of he car, and recorded in he able below. Displacemen Velociy ime x(m) v(m/s) (s)
14 (a) Plo hese daa poins on he v vs graph below, and draw he besfi sraigh lines beween each daa poin, ha is, connec each daa poin o he one before i. The acceleraion is consan or zero during each inerval lised in he daa able. (b) Lis all of he imes beween = and = 1 s a which he car is a res. (c) i. During which ime inerval is he magniude of he acceleraion of he car he greaes? ii. Wha is he value of his maximum acceleraion? (d) Find he displacemen of he car from x = a a ime of 1 s. (e) On he following graph, skech he acceleraion vs. ime graph for he moion of his car from = o = 1 s. 3
15 ANSWERS AND EXPLANATIONS TO CHAPTER REVIEW QUESTIONS Muliple Choice 1. B Displacemen is he sraighline lengh from an origin o a final posiion and includes direcion, whereas disance is simply lengh moved.. E Velociy is a vecor and herefore direcion should be included. 3. A Average speed is oal disance divided by oal ime. The oal disance covered by he jogger is 1 km and he oal ime is 1. hours, so he average speed is 1 km/hr. 4. D Δv m / s m a = = =.5 Δ 8s s 5. E v a = f v o 6m / s 4 m / s = 3s m = 6 s 6. E v f = vi + a = + / ( 4m/ s )( s) = 8 m s 33
16 7. D m x x v 1 1 f = o + o + a = (1 m) s ( 4s) = m 8. C The acceleraion due o graviy is 1 m/s a all poins during he ball s fall. 9. C Afer he ball is hrown, he only acceleraion i has is he acceleraion due o graviy, 1 m/s. 1. E A he ball s maximum heigh, v f =. Thus, v = v g = f o m s = 1 / 1 m / s = 1. s 11. D 1 1 m y = g = 1 7 s ( 1. s) = 7. m m 1. B Boh of hese graphs represen moion ha begins a a high posiive velociy, and slows down o zero velociy. 13. B The line crosses he axis (v = ) a a ime of 1 second. 14. A The objec begins wih a high negaive (backward) velociy a =, hen is speed decreases o zero by a ime of 1 s. 34
17 Free Response Quesion Soluion (a) 4 poins (b) poins The car is a res when he velociy is zero, ha is, when he graph crosses he ime axis. Thus, v = a 5 s, 9 s, and 1 s, as well as all poins beween 9 and 1 s. (c) i. 1 poin The acceleraion can be found by finding he slope of he v vs graph in a paricular inerval. The slope (acceleraion) is maximum (seepes) in he ime inerval from o 1 s. ii. poins Acceleraion = slope of v vs graph = m / s 1s s ( 4m / s) = m / s (d) 3 poins The displacemen of he car from x = can be found by deermining he area under he graph. Noe ha he area is negaive from o 5 s, and posiive from 5 s o 9 s. Don forge he iniial displacemen of m a =. Area from o 5 s = 1 squares =  1 m. Area from 5 o 1 s =.5 squares = +.5 m Toal displacemen from x = is m 1 m +.5 m = m. 35
18 (e) 3 poins 36
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. 1Dimensional Kinemaics (or 1 Dimensional moion) refers o moion in a sraigh
More informationIB 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 information2.1: 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 informationGround 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 informationPhysics 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 informationKinematics 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 informationWelcome Back to Physics 215!
Welcome Back o Physics 215! (General Physics I) Thurs. Jan 19 h, 2017 Lecure012 1 Las ime: Syllabus Unis and dimensional analysis Today: Displacemen, velociy, acceleraion graphs Nex ime: More acceleraion
More informationPHYSICS 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 informationx(m) t(sec ) Homework #2. Ph 231 Introductory Physics, Sp03 Page 1 of 4
Homework #2. Ph 231 Inroducory Physics, Sp03 Page 1 of 4 21A. 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 informationWEEK3 Recitation PHYS 131. of the projectile s velocity remains constant throughout the motion, since the acceleration a x
WEEK3 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 informationLecture 21 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 informationChapter 3 Kinematics in Two Dimensions
Chaper 3 KINEMATICS IN TWO DIMENSIONS PREVIEW Twodimensional 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 informationPhysics 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 posiionime graph is equal o he velociy of
More informationSuggested 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 informationPHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections
PHYSICS 220 Lecure 02 Moion, Forces, and Newon s Laws Texbook Secions 2.22.4 Lecure 2 Purdue Universiy, Physics 220 1 Overview Las Lecure Unis Scienific Noaion Significan Figures Moion Displacemen: Δx
More information2. 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 informationUnit 1 Test Review Physics Basics, Movement, and Vectors Chapters 13
A.P. Physics B Uni 1 Tes Reiew Physics Basics, Moemen, and Vecors Chapers 13 * In sudying for your es, make sure o sudy his reiew shee along wih your quizzes and homework assignmens. Muliple Choice Reiew:
More information1. 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. DisplacemenTime Graph Gradien = speed 1.3 VelociyTime Graph Gradien = acceleraion Area under
More informationPhysics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs.
Physics 180A Fall 2008 Tes 1120 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 informationPhys 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 informationSpeed 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 information3.6 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 informationPhysics 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 information0 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 informationOneDimensional Kinematics
OneDimensional Kinemaics One dimensional kinemaics refers o moion along a sraigh line. Een hough we lie in a 3dimension world, moion can ofen be absraced o a single dimension. We can also describe moion
More information4.5 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 informationOf 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 informationSolution: 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 informationPhysics 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 xaxis moves direcly from posiion x =. m a ime =. s o posiion x = 1. m by ime = 1. s, and hen moves direcly
More information1. 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 informationToday: 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 failsafe
More informationa 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 informationPosition, Velocity, and Acceleration
rev 06/2017 Posiion, Velociy, and Acceleraion Equipmen Qy Equipmen Par Number 1 Dynamic Track ME9493 1 Car ME9454 1 Fan Accessory ME9491 1 Moion Sensor II CI6742A 1 Track Barrier Purpose The purpose
More information1. 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 informationKinematics in One Dimension
Kinemaics in One Dimension PHY 7  dkinemaics  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 informationSPH3U: 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 informationBest 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 informationSOLUTIONS 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 informationAP 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 informationLinear Motion I Physics
Linear Moion I Physics Objecives Describe he ifference beween isplacemen an isance Unersan he relaionship beween isance, velociy, an ime Describe he ifference beween velociy an spee Be able o inerpre a
More informationEquations 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 informationToday: 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 informationMechanics Acceleration The Kinematics Equations
Mechanics Acceleraion The Kinemaics Equaions Lana Sheridan De Anza College Sep 27, 2018 Las ime kinemaic quaniies graphs of kinemaic quaniies Overview acceleraion he kinemaics equaions (consan acceleraion)
More informationPracticing 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 informationIn 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 97836600337 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 informationPhysics 101: Lecture 03 Kinematics Today s lecture will cover Textbook Sections (and some Ch. 4)
Physics 101: Lecure 03 Kinemaics Today s lecure will coer Texbook Secions 3.13.3 (and some Ch. 4) Physics 101: Lecure 3, Pg 1 A Refresher: Deermine he force exered by he hand o suspend he 45 kg mass as
More informationMEI 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 informationSPH3U1 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 posiionime and velociyime
More informationLab #2: Kinematics in 1Dimension
Reading Assignmen: Chaper 2, Secions 21 hrough 28 Lab #2: Kinemaics in 1Dimension Inroducion: The sudy of moion is broken ino wo main areas of sudy kinemaics and dynamics. Kinemaics is he descripion
More informationx 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 informationKinematics 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 1dimension some kinemaic quaniies graphs Overview velociy and speed acceleraion more graphs Kinemaics
More informationQ2.1 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 informationMotion 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 informationUniversity 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/universiphsicsmodernphsics 14hediionoungsoluionsmanual/
More information02. MOTION. Questions and Answers
CLASS09 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 informationTopic 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!!"#"$%&#'()!"#&'(*%)+,&',)./0)1*23)
"#"$%&#'()"#&'(*%)+,&',)./)1*) #$%&'()*+,&',.%,/)*+,&1*#$)()5*6$+$%*,7&*'&1*(,&*6&,7.$%$+*&%'(*8$&',,%'&1*(,&*6&,79*(&,%: ;..,*&1$&$.$%&'()*1$$.,'&',9*(&,%)?%*,('&5
More informationDynamics. 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 informationand 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 informationt A. 3. Which vector has the largest component in the ydirection, 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. Muliplechoice problems
More informationSummary:Linear Motion
Summary:Linear Moion D Saionary objec V Consan velociy D Disance increase uniformly wih ime D = v. a Consan acceleraion V D V = a. D = ½ a 2 Velociy increases uniformly wih ime Disance increases rapidly
More informationGuest Lecturer Friday! Symbolic reasoning. Symbolic reasoning. Practice Problem day A. 2 B. 3 C. 4 D. 8 E. 16 Q25. Will Armentrout.
Pracice Problem day Gues Lecurer Friday! Will Armenrou. He d welcome your feedback! Anonymously: wrie somehing and pu i in my mailbox a 111 Whie Hall. Email me: sarah.spolaor@mail.wvu.edu Symbolic reasoning
More informationChapter 2. Motion in OneDimension I
Chaper 2. Moion in OneDimension I Level : AP Physics Insrucor : Kim 1. Average Rae of Change and Insananeous Velociy To find he average velociy(v ) of a paricle, we need o find he paricle s displacemen
More informationMOMENTUM 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 information9702/1/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 informations in boxe wers ans Put
Pu answers in boxes Main Ideas in Class Toda Inroducion o Falling Appl Old Equaions Graphing Free Fall Sole Free Fall Problems Pracice:.45,.47,.53,.59,.61,.63,.69, Muliple Choice.1 Freel Falling Objecs
More informationd = ½(v o + v f) t distance = ½ (initial velocity + final velocity) time
BULLSEYE Lab Name: ANSWER KEY Dae: PreAP 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 informationAP CALCULUS AB 2003 SCORING GUIDELINES (Form B)
SCORING GUIDELINES (Form B) Quesion A blood vessel is 6 millimeers (mm) long Disance wih circular cross secions of varying diameer. x (mm) 6 8 4 6 Diameer The able above gives he measuremens of he B(x)
More informationMain Ideas in Class Today
Main Ideas in Class Toda Inroducion o Falling Appl Consan a Equaions Graphing Free Fall Sole Free Fall Problems Pracice:.45,.47,.53,.59,.61,.63,.69, Muliple Choice.1 Freel Falling Objecs Refers o objecs
More information2001 November 15 Exam III Physics 191
1 November 15 Eam III Physics 191 Physical Consans: Earh s freefall 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 information15. 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 informationSome Basic Information about MSD Systems
Some Basic Informaion abou MSD Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (nonhomogeneous) models for linear oscillaors governed by secondorder,
More informationConceptual 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 information3, so θ = arccos
Mahemaics 210 Professor Alan H Sein Monday, Ocober 1, 2007 SOLUTIONS This problem se is worh 50 poins 1 Find he angle beween he vecors (2, 7, 3) and (5, 2, 4) Soluion: Le θ be he angle (2, 7, 3) (5, 2,
More informationPhysics 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 informationPhysics 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 informationPhysics 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 informationParametrics 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 informationBrock University Physics 1P21/1P91 Fall 2013 Dr. D Agostino. Solutions for Tutorial 3: Chapter 2, Motion in One Dimension
Brock Uniersiy Physics 1P21/1P91 Fall 2013 Dr. D Agosino Soluions for Tuorial 3: Chaper 2, Moion in One Dimension The goals of his uorial are: undersand posiionime graphs, elociyime graphs, and heir
More informationPhysics 131 Fundamentals of Physics for Biologists I
10/3/2012  Fundamenals of Physics for iologiss I Professor: Wolfgang Loser 10/3/2012 Miderm review How can we describe moion (Kinemaics)  Wha is responsible for moion (Dynamics) wloser@umd.edu Movie
More informationConstant 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 informationPHYS 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 vv 0 v 0 x x v + a 1 0 0 2 0 2 Relaive Moion: Reference Frames x d Achilles Toroise x Toroise
More informationPhysics 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 informationNonuniform circular motion *
OpenSaxCNX module: m14020 1 Nonuniform circular moion * Sunil Kumar Singh This work is produced by OpenSaxCNX and licensed under he Creaive Commons Aribuion License 2.0 Wha do we mean by nonuniform
More informationTwo Coupled Oscillators / Normal Modes
Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own
More informationCHAPTER 12 DIRECT CURRENT CIRCUITS
CHAPTER 12 DIRECT CURRENT CIUITS DIRECT CURRENT CIUITS 257 12.1 RESISTORS IN SERIES AND IN PARALLEL When wo resisors are conneced ogeher as shown in Figure 12.1 we said ha hey are conneced in series. As
More information Graphing: Position Velocity. Acceleration
Tes Wednesday, Jan 31 in 101 Clark Hall a 7PM Main Ideas in Class Today  Graphing: Posiion Velociy v avg = x f f x i i a avg = v f f v i i Acceleraion Pracice ess & key online. Tes over maerial up o secion
More informationCHEAPEST 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 informationPhysics 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 informationt = 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 informationKinematics. See if you can define distance. We think you ll run into the same problem.
Kinemaics Inroducion Moion is fundamenal o our lives and o our hinking. Moving from place o place in a given amoun of ime helps define boh who we are and how we see he world. Seeing oher people, objecs
More information1.6. Slopes of Tangents and Instantaneous Rate of Change
1.6 Slopes of Tangens and Insananeous Rae of Change When you hi or kick a ball, he heigh, h, in meres, of he ball can be modelled by he equaion h() 4.9 2 v c. In his equaion, is he ime, in seconds; c represens
More informationLecture 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 informationSection 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 information72 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 informationChapter 12: Velocity, acceleration, and forces
To Feel a Force Chaper Spring, Chaper : A. Saes of moion For moion on or near he surface of he earh, i is naural o measure moion wih respec o objecs fixed o he earh. The 4 hr. roaion of he earh has a measurable
More informationQ.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 informationAP Physics 1  Summer Assignment
AP Physics 1  Summer Assignmen This assignmen is due on he firs day of school. You mus show all your work in all seps. Do no wai unil he las minue o sar his assignmen. This maerial will help you wih he
More informationThe average rate of change between two points on a function is d t
SM Dae: Secion: Objecive: The average rae of change beween wo poins on a funcion is d. For example, if he funcion ( ) represens he disance in miles ha a car has raveled afer hours, hen finding he slope
More information