AP CALCULUS AB 2004 SCORING GUIDELINES (Form B)
|
|
- Zoe Blake
- 5 years ago
- Views:
Transcription
1 4 SCORING GUIDELINES (Form B) Quesion A es plane flies in a sraigh line wih (min) posiive velociy v (), in miles per v ()(mpm) minue a ime minues, where v is a differeniable funcion of. Seleced values of v () for 4 are shown in he able above. (a) Use a midpoin Riemann sum wih four subinervals of equal lengh and values from he able o 4 approximae v () d. Show he compuaions ha lead o your answer. Using correc unis, 4 explain he meaning of v () din erms of he plane s fligh. (b) Based on he values in he able, wha is he smalles number of insances a which he acceleraion of he plane could equal zero on he open inerval < < 4? Jusify your answer. 7 (c) The funcion f, defined by f() = 6 + cos( ) + sin ( ), is used o model he velociy of he 1 4 plane, in miles per minue, for 4. According o his model, wha is he acceleraion of he plane a =? Indicaes unis of measure. (d) According o he model f, given in par (c), wha is he average velociy of he plane, in miles per minue, over he ime inerval 4? (a) Midpoin Riemann sum is 1 [ v( 5) + v( 15) + v( 5) + v( 5) ] = 1 [ ] = 9 The inegral gives he oal disance in miles ha he plane flies during he 4 minues. : 1 : v( 5) + v( 15) + v( 5) + v( 5) 1 : answer 1 : meaning wih unis (b) By he Mean Value Theorem, v () = somewhere in he inerval (, 15 ) and somewhere in he inerval ( 5, ). Therefore he acceleraion will equal for a leas wo values of. 1 : wo insances : 1 : jusificaion (c) f ( ) =.47 or.48 miles per minue 1 : answer wih unis 1 4 (d) Average velociy = () 4 f d = miles per minue : 1 : limis 1 : inegrand 1 : answer Copyrigh 4 by College Enrance Examinaion Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and (for AP sudens and parens). 46 4
2 6 SCORING GUIDELINES (Form B) Quesion 6 (sec) v () ( f sec ) a () ( f sec ) A car ravels on a sraigh rack. During he ime inerval 6 seconds, he car s velociy v, measured in fee per second, and acceleraion a, measured in fee per second per second, are coninuous funcions. The able above shows seleced values of hese funcions. (a) Using appropriae unis, explain he meaning of v () din erms of he car s moion. Approximae 6 v () dusing a rapezoidal approximaion wih he hree subinervals deermined by he able. 6 (b) Using appropriae unis, explain he meaning of a () din erms of he car s moion. Find he exac value of a () d. (c) For < < 6, mus here be a ime when v () = 5? Jusify your answer. (d) For < < 6, mus here be a ime when a () =? Jusify your answer. 6 (a) v () dis he disance in fee ha he car ravels from = sec o = 6 sec. Trapezoidal approximaion for v () 6 d: A = ( ) 5 + ( 1)( 15) + ( 1)( 1) = 185 f (b) a () dis he car s change in velociy in f/sec from = sec o = sec. a () d= v () d= v( ) v( ) = 14 ( ) = 6 f/sec (c) Yes. Since v( 5) = 1 < 5 < = v( 5 ), he IVT guaranees a in ( 5, 5 ) so ha v () = 5. (d) Yes. Since v( ) = v( 5 ), he MVT guaranees a in (, 5 ) so ha a () = v () =. Unis of f in (a) and f/sec in (b) : { 1 : explanaion 1 : value : { 1 : explanaion 1 : value 1 : v( 5) < 5 < v( 5) : 1 : Yes; refers o IVT or hypoheses 1 : v( ) = v( 5) : 1 : Yes; refers o MVT or hypoheses 1 : unis in (a) and (b) 6 The College Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and (for AP sudens and parens). 7 48
3 6 SCORING GUIDELINES Quesion 4 (seconds) v () (fee per second) Rocke A has posiive velociy v () afer being launched upward from an iniial heigh of fee a ime = seconds. The velociy of he rocke is recorded for seleced values of over he inerval 8 seconds, as shown in he able above. (a) Find he average acceleraion of rocke A over he ime inerval 8 seconds. Indicae unis of measure. 7 (b) Using correc unis, explain he meaning of v () din erms of he rocke s fligh. Use a midpoin Riemann sum wih subinervals of equal lengh o approximae v () d. 1 (c) Rocke B is launched upward wih an acceleraion of a () = fee per second per second. A ime + 1 = seconds, he iniial heigh of he rocke is fee, and he iniial velociy is fee per second. Which of he wo rockes is raveling faser a ime = 8 seconds? Explain your answer. 7 1 (a) Average acceleraion of rocke A is 1 : answer v( 8) v( ) f sec = = 8 8 (b) Since he velociy is posiive, v () drepresens he disance, in fee, raveled by rocke A from = 1 seconds o = 7 seconds : explanaion : 1 : uses v( ), v( 4 ), v( 6) 1 : value A midpoin Riemann sum is [ v( ) + v( 4) + v( 6) ] = [ ] = f (c) Le vb () be he velociy of rocke B a ime. vb () = d = C + 1 = v ( ) = 6 + C B vb () = v ( 8) = 5 > 49 = v( 8) B 4 : 1 : : consan of inegraion 1 : uses iniial condiion 1 : finds vb ( 8 ), compares o v( 8 ), and draws a conclusion Rocke B is raveling faser a ime = 8 seconds. Unis of f sec in (a) and f in (b) 1 : unis in (a) and (b) 6 The College Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and (for AP sudens and parens). 5 49
4
5
6
7 SCORING GUIDELINES (Form B) Quesion )F=HJE?ALAI=CJDAN=NEIIJD=JEJILA?EJOL=J=OJEAJBH > J > $ EICELA>O IEJ LJ A Г)JJEAJJDAF=HJE?AEI=JJDAHECE = JDA=NAIFHLE@A@IAJ?DJDACH=FDBLJ BH > J > $ >,KHECMD=JEJAHL=IBJEAEIJDAF=HJE?ALECJJDAABJ/ELA=HA=IBHOKH 1IJDAHA=OJEAJ J > $ =JMDE?DJDAF=HJE?AHAJKHIJJDAHECEKIJEBOOKH = LJ =IMAH > =HJE?AEILECJJDAABJMDA LJ EA A IE?! " =@# $ H " LJ IEJ LJ Г JHJ N $#$ N" " J N ГN N" ГN 6DAHAEIIK?DJEA>A?=KIA 6 BH=6 J CH=FD Copyrigh by College Enrance Examinaion Board. All righs reserved. Advanced Placemen Program and AP are regisered rademarks of he College Enrance Examinaion Board. 4 JDHAA]DKFI^ FAHE@E?>AD=LEH IJ=HJI=JHECE HA=I=>AHA=JELA=N=@EL=KAI EJAHL=I! Г A=?DEIIECHE?HHA?JEJAHL= HA=I EEJIB=@"=EJACH=B LJ H LJ H KIAIN=@N"J?FKJA@EIJ=?A! D=@AI?D=CAB@EHA?JE=JIJK@AJ\I JKHECFEJ =IMAH JAEBE?HHA?JJKHECFEJ IK?DJEA HA=I 97
8 SCORING GUIDELINES Quesion )>A?JLAI=CJDA N=NEIMEJDEEJE=FIEJE N 6DALA?EJOBJDA>A?J=JJEA J F EICELA >O L J IE J! = 9D=JEIJDA=??AAH=JEBJDA>A?J=JJEA J " > +IE@AHJDABMECJMIJ=JAAJI 5J=JAAJ1.H! J "#JDALA?EJOBJDA>A?JEI@A?HA=IEC 5J=JAAJ11.H! J "#JDAIFAA@BJDA>A?JEIE?HA=IEC )HAAEJDAHH>JDBJDAIAIJ=JAAJI?HHA?J.HA=?DIJ=JAAJFHLE@A=HA=IMDOEJEI?HHA?JHJ?HHA?J? 9D=JEIJDAJJ=@EIJ=?AJH=LAA@>OJDA>A?JLAHJDAJEAEJAHL= > J > 9D=JEIJDAFIEJEBJDA>A?J=JJEA J " " = = " L= "?I!! Г HГ#! HГ# " $ =IMAH >! J "# =J L= J?I J!! 5J=JAAJ1EI?HHA?JIE?A=J 5J=JAAJ11EI?HHA?JIE?A LJ =@ =J?,EIJ=?A " 4!! NJ Г?I J! N N" '!"!!' LJ MDAJ! $ N!!''&$ N! ГN N" ГN! N" N 4!! NJ Г?I J! N" '!"! " Copyrigh by College Enrance Examinaion Board. All righs reserved. Advanced Placemen Program and AP are regisered 98 rademarks of he College Enrance Examinaion Board. 4 1?HHA?JMEJDHA=I! 11?HHA?J HA=IBH11 EEJIB=@"=EJACH= BLJ H LJ H D=@AI?D=CAB@EHA?JE=J IJK@AJ\IJKHECFEJ =IMAH EBE?HHA?JJKHECFEJH JKHECFEJ EJACH= =IMAH 4! NJ Г?I J +! =IMAH EB?IJ=JBEJACH=JE
9 SCORING GUIDELINES (Form B) Quesion 4 A paricle moves along he x-axis wih velociy a ime given by v( ) = 1 + e1. (a) Find he acceleraion of he paricle a ime =. (b) Is he speed of he paricle increasing a ime =? Give a reason for your answer. (c) Find all values of a which he paricle changes direcion. Jusify your answer. (d) Find he oal disance raveled by he paricle over he ime inerval. 1 (a) a () = v() = e a() = e : 1 : v( ) 1 : a() (b) a () < e v() = 1 + < Speed is increasing since v () < and a () <. 1 : answer wih reason 1 (c) v () = when 1 = e, so = 1. v () > for < 1 and v () < for > 1. Therefore, he paricle changes direcion a = 1. : 1 : solves v ( ) = o ge = 1 1 : jusifies change in direcion a = 1 (d) Disance = v () d = ( ) + ( + ) = ( 1+ ) + ( 1 ) e d e d e e 1 = ( 1 1+ e) + ( + e 1 1) 4 : 1 : limis 1 : inegrand 1 : anidiffereniaion 1 : evaluaion = e + 1 e OR OR 1 () = x e x() = e x (1) = e x() = Disance = ( x(1) x() ) + ( x(1) x() ) = ( + e) + ( 1+ e ) = e + 1 e 4 : 1 : any aniderivaive 1 : evaluaes x ( ) when =, 1, 1 : evaluaes disance beween poins 1 : evaluaes oal disance Copyrigh by College Enrance Examinaion Board. All righs reserved. Available a apcenral.collegeboard.com. 99 5
10 SCORING GUIDELINES Quesion A paricle moves along he x-axis so ha is velociy a ime is given by A ime =, he paricle is a posiion x = 1. v( ) = ( + 1) sin. (a) Find he acceleraion of he paricle a ime =. Is he speed of he paricle increasing a =? Why or why no? (b) Find all imes in he open inerval < < when he paricle changes direcion. Jusify your answer. (c) Find he oal disance raveled by he paricle from ime = unil ime =. (d) During he ime inerval, wha is he greaes disance beween he paricle and he origin? Show he work ha leads o your answer. (a) a() = v() = or v () = sin() < Speed is decreasing since a () > and v () <. : 1: a() 1: speed decreasing wih reason (b) v () = when = = or.56 or.57 Since v () < for < < and v () > for < <, he paricle changes direcions a =. : 1: = only 1: jusificaion (c) Disance = v () d = 4. or 4.4 : 1: limis 1: inegrand 1: answer (d) v () d=.65 x( ) = x() + v( ) d =.65 Since he oal disance from = o = is : 1: ± (disance paricle ravels while velociy is negaive) 1 : answer 4.4, he paricle is sill o he lef of he origin a =. Hence he greaes disance from he origin is.65. Copyrigh by College Enrance Examinaion Board. All righs reserved. Available a apcenral.collegeboard.com. 1
11 4 SCORING GUIDELINES Quesion A paricle moves along he y-axis so ha is velociy v a ime A ime =, he paricle is a y = 1. (Noe: an (a) Find he acceleraion of he paricle a ime =. 1 x = arcan x ) 1 is given by v () = ( e) 1 an. (b) Is he speed of he paricle increasing or decreasing a ime =? Give a reason for your answer. (c) Find he ime a which he paricle reaches is highes poin. Jusify your answer. (d) Find he posiion of he paricle a ime =. Is he paricle moving oward he origin or away from he origin a ime =? Jusify your answer. (a) a( ) = v ( ) =.1 or.1 1 : answer (b) v ( ) =.46 Speed is increasing since a ( ) < and v ( ) <. 1 : answer wih reason 1 v = when ( e ) (c) () an = 1 = ln ( an () 1 ) =.44 is he only criical value for y. v () > for < < ln ( an () 1 ) v () < for > ln ( an () 1 ) 1 : ses v () = : 1 : idenifies =.44 as a candidae 1 : jusifies absolue maximum y () has an absolue maximum a =.44. (d) y( ) = 1+ v( ) d = 1.6 or 1.61 The paricle is moving away from he origin since v ( ) < and y ( ) <. 4 : 1 : v () d 1 : handles iniial condiion 1 : value of y( ) 1 : answer wih reason Copyrigh 4 by College Enrance Examinaion Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and (for AP sudens and parens). 11 4
12 5 SCORING GUIDELINES (Form B) Quesion A paricle moves along he x-axis so ha is velociy v a ime, for 5, is given by () ( ) v = ln +. The paricle is a posiion x = 8 a ime =. (a) Find he acceleraion of he paricle a ime = 4. (b) Find all imes in he open inerval < < 5 a which he paricle changes direcion. During which ime inervals, for 5, does he paricle ravel o he lef? (c) Find he posiion of he paricle a ime =. (d) Find he average speed of he paricle over he inerval. 5 (a) a( 4) = v ( 4) = 1 : answer 7 (b) v () = + = 1 + = ( ) ( 1) = = 1, 1 : ses v () = : 1 : direcion change a = 1, 1 : inerval wih reason v () > for < < 1 v () < for 1 < < v () > for < < 5 The paricle changes direcion when = 1 and =. The paricle ravels o he lef when 1 < <. (c) () = ( ) + ln( + ) ( ) = 8 + ln( + ) s s u u du s u u du = 8.68 or 8.69 : ( ) 1 : ln u u + du 1 : handles iniial condiion 1 : answer 1 (d) () v d=.7 or.71 1 : inegral : 1 : answer Copyrigh 5 by College Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and (for AP sudens and parens). 1 4
13 7 SCORING GUIDELINES (Form B) Quesion A paricle moves along he x-axis so ha is velociy v a ime is given by v sin. The graph of v is shown above for 5. The posiion of he paricle a ime is x and is posiion a ime is x 5. (a) Find he acceleraion of he paricle a ime. (b) Find he oal disance raveled by he paricle from ime o. (c) Find he posiion of he paricle a ime. (d) For 5, find he ime a which he paricle is farhes o he righ. Explain your answer. (a) a v 6cos or (b) Disance v d 1.7 OR For, v when and.566 x 5 x x 5 v d v d x 5 v d x x x x x x : a : 1 : seup 1 : answer 1 : inegrand (c) x 5 v d 5.77 or : 1 : uses x 5 1 : answer (d) The paricle s righmos posiion occurs a ime The paricle changes from moving righ o moving lef a hose imes for which v wih v changing from posiive o negaive, namely a,, ,.7,.96. T Using xt 5 v d, he paricle s posiions a he imes i changes from righward o lefward movemen are: T: 5 xt : The paricle is farhes o he righ when T. : 1 : ses v 1 : answer 1 : reason 7 The College Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and (for sudens and parens). 1
14 7 SCORING GUIDELINES Quesion 4 A paricle moves along he x-axis wih posiion a ime given by x() = e sin for π. (a) Find he ime a which he paricle is farhes o he lef. Jusify your answer. (b) Find he value of he consan A for which x() saisfies he equaion Ax () + x () + x() = for < < π. (a) () sin x = e + e cos = e ( cos sin ) x () = when cos = sin. Therefore, x () = on π 5 π π for = and =. 4 4 The candidaes for he absolue minimum are a π 5π,,, and π : : x () 1 : ses x () = 1 : answer 1: jusificaion x() e sin ( ) = π 4 5π 4 e e π π ( 4 ) > π ( ) 4 sin 5π 4 5 sin < 4 π e π sin ( π ) = The paricle is farhes o he lef when = 5 π. 4 (b) x () = e ( cos sin ) + e ( sin cos ) = e cos Ax () + x () + x() ( ) ( ) = A e cos + e cos sin + e sin = ( A + 1) e cos = 4 : : x () 1 : subsiues x (), x (), and x() ino Ax () + x () + x() 1 : answer Therefore, A = 1. 7 The College Board. All righs reserved. Visi apcenral.collegeboard.com (for AP professionals) and (for sudens and parens). 14
15
16
17
18
2017 AP CALCULUS AB FREE-RESPONSE QUESTIONS
17 FREE-RESPONSE QUESTIONS 5. Two paricles move along he x-axis. For 8, he posiion of paricle P a ime is given by xp () ln ( 1 ), while he velociy of paricle Q a ime is given by vq () 8 15. Paricle Q is
More informationAP CALCULUS AB 2017 SCORING GUIDELINES
AP CALCULUS AB 17 SCORING GUIDELINES 16 SCORING GUIDELINES Quesion For, a paricle moves along he x-axis. The velociy of he paricle a ime is given by v ( ) = 1 + sin. The paricle is a posiion x = a ime.
More informationAP 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 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 informationAP CALCULUS AB 2003 SCORING GUIDELINES (Form B)
SCING GUIDELINES (Form B) Quesion 4 A paricle moves along he x-axis wih velociy a ime given by v( ) = 1 + e1. (a) Find he acceleraion of he paricle a ime =. (b) Is he speed of he paricle increasing a ime
More information1998 Calculus AB Scoring Guidelines
AB{ / BC{ 1999. The rae a which waer ows ou of a pipe, in gallons per hour, is given by a diereniable funcion R of ime. The able above shows he rae as measured every hours for a {hour period. (a) Use a
More informationAP CALCULUS AB 2017 SCORING GUIDELINES
AP CALCULUS AB 17 SCORING GUIDELINES /CALCULUS BC 15 SCORING GUIDELINES Quesion (minues) v ( ) (meers per minue) 1 4 4 4 15 Johanna jogs along a sraigh pah. For 4, Johanna s velociy is given by a differeniable
More informationAP 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 informationAP CALCULUS AB/CALCULUS BC 2016 SCORING GUIDELINES. Question 1
AP CALCULUS AB/CALCULUS BC 6 SCORING GUIDELINES Quesion (hours) R ( ) (liers / hour) 6 4 9 95 74 7 Waer is pumped ino a ank a a rae modeled by W( ) = e liers per hour for, where is measured in hours. Waer
More informationAP CALCULUS AB 2003 SCORING GUIDELINES (Form B)
SCORING GUIDELINES (Form B) Quesion A ank conains 15 gallons of heaing oil a ime =. During he ime inerval 1 hours, heaing oil is pumped ino he ank a he rae 1 H ( ) = + ( 1 + ln( + 1) ) gallons per hour.
More informationAP 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 informationAP Calculus BC - Parametric equations and vectors Chapter 9- AP Exam Problems solutions
AP Calculus BC - Parameric equaions and vecors Chaper 9- AP Exam Problems soluions. A 5 and 5. B A, 4 + 8. C A, 4 + 4 8 ; he poin a is (,). y + ( x ) x + 4 4. e + e D A, slope.5 6 e e e 5. A d hus d d
More informationAP CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES. Question 1
AP CALCULUS AB/CALCULUS BC 15 SCORING GUIDELINES Quesion 1 The rae a which rainwaer flows ino a drainpipe is modeled by he funcion R, where R ( ) = sin 5 cubic fee per hour, is measured in hours, and 8.
More informationMultiple Choice Solutions 1. E (2003 AB25) () xt t t t 2. A (2008 AB21/BC21) 3. B (2008 AB7) Using Fundamental Theorem of Calculus: 1
Paricle Moion Soluions We have inenionally included more maerial han can be covered in mos Suden Sudy Sessions o accoun for groups ha are able o answer he quesions a a faser rae. Use your own judgmen,
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 information!!"#"$%&#'()!"#&'(*%)+,&',-)./0)1-*23)
"#"$%&#'()"#&'(*%)+,&',-)./)1-*) #$%&'()*+,&',-.%,/)*+,-&1*#$)()5*6$+$%*,7&*-'-&1*(,-&*6&,7.$%$+*&%'(*8$&',-,%'-&1*(,-&*6&,79*(&,%: ;..,*&1$&$.$%&'()*1$$.,'&',-9*(&,%)?%*,('&5
More informationAP CALCULUS AB 2017 SCORING GUIDELINES
AP CALCULUS AB 17 SCORING GUIDELINES /CALCULUS BC 16 SCORING GUIDELINES Quesion 1 (hours) R ( ) (liers / hour) 1 6 8 14 119 95 74 7 Waer is pumped ino a ank a a rae modeled by W( ) = e liers per hour for
More informationAnswers to 1 Homework
Answers o Homework. x + and y x 5 y To eliminae he parameer, solve for x. Subsiue ino y s equaion o ge y x.. x and y, x y x To eliminae he parameer, solve for. Subsiue ino y s equaion o ge x y, x. (Noe:
More informationAP CALCULUS AB 2017 SCORING GUIDELINES
AP CALCULUS AB 07 SCORING GUIDELINES 06 SCORING GUIDELINES Question 6 f ( ) f ( ) g( ) g ( ) 6 8 0 8 7 6 6 5 The functions f and g have continuous second derivatives. The table above gives values of the
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 informationCALCULUS EXPLORATION OF THE SECOND FUNDAMENTAL THEOREM OF CALCULUS. Second Fundamental Theorem of Calculus (Chain Rule Version):
CALCULUS EXPLORATION OF THE SECOND FUNDAMENTAL THEOREM OF CALCULUS 6 cos Secon Funamenal Theorem of Calculus: f a 4 a f 6 cos Secon Funamenal Theorem of Calculus (Chain Rule Version): g f a E. Use he Secon
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 informationKINEMATICS 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 informationMath 115 Final Exam December 14, 2017
On my honor, as a suden, I have neiher given nor received unauhorized aid on his academic work. Your Iniials Only: Iniials: Do no wrie in his area Mah 5 Final Exam December, 07 Your U-M ID # (no uniqname):
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 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 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 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 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 informationMEI STRUCTURED MATHEMATICS 4758
OXFORD CAMBRIDGE AND RSA EXAMINATIONS Advanced Subsidiary General Cerificae of Educaion Advanced General Cerificae of Educaion MEI STRUCTURED MATHEMATICS 4758 Differenial Equaions Thursday 5 JUNE 006 Afernoon
More informationx(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 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 information4.6 One Dimensional Kinematics and Integration
4.6 One Dimensional Kinemaics and Inegraion When he acceleraion a( of an objec is a non-consan funcion of ime, we would like o deermine he ime dependence of he posiion funcion x( and he x -componen of
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 posiion-ime graph is equal o he velociy of
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 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 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 informationMath 116 Second Midterm March 21, 2016
Mah 6 Second Miderm March, 06 UMID: EXAM SOLUTIONS Iniials: Insrucor: Secion:. Do no open his exam unil you are old o do so.. Do no wrie your name anywhere on his exam. 3. This exam has pages including
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 informationWEEK-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 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 informationACCUMULATION. Section 7.5 Calculus AP/Dual, Revised /26/2018 7:27 PM 7.5A: Accumulation 1
ACCUMULATION Secion 7.5 Calculus AP/Dual, Revised 2019 vie.dang@humbleisd.ne 12/26/2018 7:27 PM 7.5A: Accumulaion 1 APPLICATION PROBLEMS A. Undersand he quesion. I is ofen no necessary o as much compuaion
More informationMath 116 Practice for Exam 2
Mah 6 Pracice for Exam Generaed Ocober 3, 7 Name: SOLUTIONS Insrucor: Secion Number:. This exam has 5 quesions. Noe ha he problems are no of equal difficuly, so you may wan o skip over and reurn o a problem
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 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 informationDisplacement ( 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 informationUCLA: 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 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 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 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 informationSome Basic Information about M-S-D Systems
Some Basic Informaion abou M-S-D Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (non-homogeneous) models for linear oscillaors governed by second-order,
More informationVariable 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 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 informationWelcome 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 informationLecture 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 informationHOMEWORK # 2: MATH 211, SPRING Note: This is the last solution set where I will describe the MATLAB I used to make my pictures.
HOMEWORK # 2: MATH 2, SPRING 25 TJ HITCHMAN Noe: This is he las soluion se where I will describe he MATLAB I used o make my picures.. Exercises from he ex.. Chaper 2.. Problem 6. We are o show ha y() =
More informationd = 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 informationu(x) = e x 2 y + 2 ) Integrate and solve for x (1 + x)y + y = cos x Answer: Divide both sides by 1 + x and solve for y. y = x y + cos x
. 1 Mah 211 Homework #3 February 2, 2001 2.4.3. y + (2/x)y = (cos x)/x 2 Answer: Compare y + (2/x) y = (cos x)/x 2 wih y = a(x)x + f(x)and noe ha a(x) = 2/x. Consequenly, an inegraing facor is found wih
More informationWeek #13 - Integration by Parts & Numerical Integration Section 7.2
Week #3 - Inegraion by Pars & Numerical Inegraion Secion 7. From Calculus, Single Variable by Hughes-Halle, Gleason, McCallum e. al. Copyrigh 5 by John Wiley & Sons, Inc. This maerial is used by permission
More informationThe Fundamental Theorem of Calculus Solutions
The Fundamenal Theorem of Calculus Soluions We have inenionally included more maerial han can be covered in mos Suden Sudy Sessions o accoun for groups ha are able o answer he quesions a a faser rae. Use
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 informationSection 3.8, Mechanical and Electrical Vibrations
Secion 3.8, Mechanical and Elecrical Vibraions Mechanical Unis in he U.S. Cusomary and Meric Sysems Disance Mass Time Force g (Earh) Uni U.S. Cusomary MKS Sysem CGS Sysem fee f slugs seconds sec pounds
More informationPROBLEMS FOR MATH 162 If a problem is starred, all subproblems are due. If only subproblems are starred, only those are due. SLOPES OF TANGENT LINES
PROBLEMS FOR MATH 6 If a problem is sarred, all subproblems are due. If onl subproblems are sarred, onl hose are due. 00. Shor answer quesions. SLOPES OF TANGENT LINES (a) A ball is hrown ino he air. Is
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 2.2-2.4 Lecure 2 Purdue Universiy, Physics 220 1 Overview Las Lecure Unis Scienific Noaion Significan Figures Moion Displacemen: Δx
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 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 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 informationUnit 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 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 information(π 3)k. f(t) = 1 π 3 sin(t)
Mah 6 Fall 6 Dr. Lil Yen Tes Show all our work Name: Score: /6 No Calculaor permied in his par. Read he quesions carefull. Show all our work and clearl indicae our final answer. Use proper noaion. Problem
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. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under
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 information1 1 + x 2 dx. tan 1 (2) = ] ] x 3. Solution: Recall that the given integral is improper because. x 3. 1 x 3. dx = lim dx.
. Use Simpson s rule wih n 4 o esimae an () +. Soluion: Since we are using 4 seps, 4 Thus we have [ ( ) f() + 4f + f() + 4f 3 [ + 4 4 6 5 + + 4 4 3 + ] 5 [ + 6 6 5 + + 6 3 + ]. 5. Our funcion is f() +.
More informationA. Using Newton s second law in one dimension, F net. , write down the differential equation that governs the motion of the block.
Simple SIMPLE harmonic HARMONIC moion MOTION I. Differenial equaion of moion A block is conneced o a spring, one end of which is aached o a wall. (Neglec he mass of he spring, and assume he surface is
More informationMidterm Exam Review Questions Free Response Non Calculator
Name: Dae: Block: Miderm Eam Review Quesions Free Response Non Calculaor Direcions: Solve each of he following problems. Choose he BEST answer choice from hose given. A calculaor may no be used. Do no
More informationMATH 4330/5330, Fourier Analysis Section 6, Proof of Fourier s Theorem for Pointwise Convergence
MATH 433/533, Fourier Analysis Secion 6, Proof of Fourier s Theorem for Poinwise Convergence Firs, some commens abou inegraing periodic funcions. If g is a periodic funcion, g(x + ) g(x) for all real x,
More informationTopics covered in tutorial 01: 1. Review of definite integrals 2. Physical Application 3. Area between curves. 1. Review of definite integrals
MATH4 Calculus II (8 Spring) MATH 4 Tuorial Noes Tuorial Noes (Phyllis LIANG) IA: Phyllis LIANG Email: masliang@us.hk Homepage: hps://masliang.people.us.hk Office: Room 3 (Lif/Lif 3) Phone number: 3587453
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 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 informationApplications of the Basic Equations Chapter 3. Paul A. Ullrich
Applicaions of he Basic Equaions Chaper 3 Paul A. Ullrich paullrich@ucdavis.edu Par 1: Naural Coordinaes Naural Coordinaes Quesion: Why do we need anoher coordinae sysem? Our goal is o simplify he equaions
More informationChapter Let. 1) k be a vector-valued function. (a) Evaluate f (0). (b) What is the domain of f () t? (c) Is f () t continuous at t = 1?
Chaper. Le f() = sin i+ ( 3+ ) j ln( + ) k be a vecor-valued funcion. (a) Evaluae f (). (b) Wha is he domain of f ()? (c) Is f () coninuous a =? Chaper. Le f() = sin i+ ( 3+ ) j ln( + ) k be a vecor-valued
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 informationv x + v 0 x v y + a y + v 0 y + 2a y + v y Today: Projectile motion Soccer problem Firefighter example
Thurs Sep 10 Assign 2 Friday SI Sessions: Moron 227 Mon 8:10-9:10 PM Tues 8:10-9:10 PM Thur 7:05-8:05 PM Read Read Draw/Image lay ou coordinae sysem Wha know? Don' know? Wan o know? Physical Processes?
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 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 fail-safe
More informationRobotics I. April 11, The kinematics of a 3R spatial robot is specified by the Denavit-Hartenberg parameters in Tab. 1.
Roboics I April 11, 017 Exercise 1 he kinemaics of a 3R spaial robo is specified by he Denavi-Harenberg parameers in ab 1 i α i d i a i θ i 1 π/ L 1 0 1 0 0 L 3 0 0 L 3 3 able 1: able of DH parameers of
More informationPrinciple of Least Action
The Based on par of Chaper 19, Volume II of The Feynman Lecures on Physics Addison-Wesley, 1964: pages 19-1 hru 19-3 & 19-8 hru 19-9. Edwin F. Taylor July. The Acion Sofware The se of exercises on Acion
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 informationSMT 2014 Calculus Test Solutions February 15, 2014 = 3 5 = 15.
SMT Calculus Tes Soluions February 5,. Le f() = and le g() =. Compue f ()g (). Answer: 5 Soluion: We noe ha f () = and g () = 6. Then f ()g () =. Plugging in = we ge f ()g () = 6 = 3 5 = 5.. There is a
More informationPHYS 100: Lecture 2. Motion at Constant Acceleration. Relative Motion: Reference Frames. x Tortoise. Tortoise. d Achilles. Reference frame = Earth
a PHYS 1: Lecure 2 Moion a Consan Acceleraion a Area = a a v = ad v v = a v x = vd A=(1/2)( v) Area = v v = v-v v x x = v + a 1 2 2 Relaive Moion: Reference Frames x d Achilles Toroise x Toroise Reference
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/universi-phsics-modern-phsics- 14h-ediion-oung-soluions-manual-/
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 1-dimension some kinemaic quaniies graphs Overview velociy and speed acceleraion more graphs Kinemaics
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 informationMATH 128A, SUMMER 2009, FINAL EXAM SOLUTION
MATH 28A, SUMME 2009, FINAL EXAM SOLUTION BENJAMIN JOHNSON () (8 poins) [Lagrange Inerpolaion] (a) (4 poins) Le f be a funcion defined a some real numbers x 0,..., x n. Give a defining equaion for he Lagrange
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 informationk 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 informationTesting What You Know Now
Tesing Wha You Know Now To bes each you, I need o know wha you know now Today we ake a well-esablished quiz ha is designed o ell me his To encourage you o ake he survey seriously, i will coun as a clicker
More informationRoller-Coaster Coordinate System
Winer 200 MECH 220: Mechanics 2 Roller-Coaser Coordinae Sysem Imagine you are riding on a roller-coaer in which he rack goes up and down, wiss and urns. Your velociy and acceleraion will change (quie abruply),
More informationInstructor: Barry McQuarrie Page 1 of 5
Procedure for Solving radical equaions 1. Algebraically isolae one radical by iself on one side of equal sign. 2. Raise each side of he equaion o an appropriae power o remove he radical. 3. Simplify. 4.
More informationWELCOME TO 1103 PERIOD 3. Homework Exercise #2 is due at the beginning of class. Please put it on the stool in the front of the classroom.
WELCOME TO 1103 PERIOD 3 Homework Exercise #2 is due a he beginning of class. Please pu i on he sool in he fron of he classroom. Ring of Truh: Change 1) Give examples of some energy ransformaions in he
More information