Answer, Key Homework 2 David McIntyre Mar 25,

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1 Answer, Key Homework 2 Daid McInyre 4123 Mar 2, This prin-ou should hae 1 quesions. Muliple-choice quesions may coninue on he ne column or page find all choices before making your selecion. The due ime is Cenral ime. Chaper 2 problems. 001 (par 1 of 1) 0 poins The graph below shows he elociy as a funcion of ime for an objec moing in a sraigh line. Which of he following graphs shows he corresponding displacemen as a funcion of ime for he same ime ineral? zero a firs, hen remains consan, hen decreases linearly o zero, he displacemen will increase a firs proporional o ime squared, hen increase linearly, and hen increase proporional o negaie ime squared. From hese facs, we can obain he correc answer. 002 (par 1 of 2) poins A paricle moes according o he equaion = (10 m/s 2 ) 2 where is in meers and is in seconds. Find he aerage elociy for he ime ineral from 1 = 2.1 s o 2 = 3.9 s. Correc answer: 60. m/s. ae = = (10 m/s 2 ) 2 = (10 m/s2 ) ( ) 2 1 = (10 m/s2 ) [(3.9 s) 2 (2.1 s) 2 ] (3.9 s) (2.1 s) = 60. m/s (par 2 of 2) poins Find he aerage elociy for he ime ineral from 1 = 2.1 s o 3 = 2.2 s. Correc answer: 43 m/s. correc. The displacemen is he inegral of he elociy wih respec o ime = d. Because he elociy increases linearly from ae = = (10 m/s2 ) ( ) 3 1 = (10 m/s2 ) [(2.2 s) 2 (2.1 s) 2 ] (2.2 s) (2.1 s) = 43 m/s 004 (par 1 of 1) 0 poins The acceleraion of an objec, saring from res, is shown on he graph below.

2 Answer, Key Homework 2 Daid McInyre 4123 Mar 2, a(m/s 2 ) (s) her han a = 0, when is he elociy of he objec equal o zero? 1..0 s s s 4. A no oher ime on his graph. correc. During he ineral from 1.0 s o 3.0 s. Since = 0 a d, is he area beween he acceleraion cure and he ais during he ime period from 0 o. If he area is aboe he horizonal ais, i is posiie; oherwise, i is negaie. In order for he elociy o be zero a any gien ime, here would hae o be equal amouns of posiie and negaie area beween 0 and. According o he graph, his condiion is neer saisfied. 00 (par 1 of 1) 0 poins Idenify all of hose graphs ha represen moion a consan speed (noe he aes carefully). a) b) a c) d) a e) 1. (e) only 2. (a) and (d) correc 3. (a), (b), and (e) 4. (a), (b), and (d). (a), (b), and (c) 6. (a) only 7. (a) and (c) 8. None of hese 9. (c) only 10. (d) only Basic Conceps: = o and a = 0. Soluion: a) = k, k > 0 is a linear funcion of, so i is correc. b) = k, k > 0 increases a a consan rae, so i is incorrec. c) a = k, k > 0, so i is incorrec. d) = k, k > 0, so i is correc. e) a = k, k > 0, so i is incorrec.

3 Answer, Key Homework 2 Daid McInyre 4123 Mar 2, (par 1 of 1) 0 poins A car moes along a sraigh line. The graph below shows is elociy as a funcion of ime. elociy P ime Which of he following saemens correcly describes he car s moion a poin P on he graph? Cauion: selec only one answer (whicheer you hink is mos appropriae). 1. The car s direcion is abou 4 off he ais. 2. The car is saionary. 3. The car is acceleraing. correc 4. The car is climbing a hill.. The car has zero acceleraion. 6. The car is deceleraing. Noe: The graph depics he elociy () as a funcion of ime and no he posiion (). A poin P on he graph, he elociy is posiie (indeed, 0 a all imes depiced on he graph) and he cure () slopes upward which means posiie deriaie d d > 0. In oher words, he car has posiie acceleraion a = d > 0. Since > 0, his means he d car is acceleraing. 007 (par 1 of 3) 4 poins Two moorcycle cops are posiioned ogeher on I3S. Each is capable of a maimum speed of 279 km/hr. They sar from res and uniformly accelerae o maimum speed oer a disance of 3 km. Wha is he acceleraion of each moorcycle? ( acc is he ime i akes each moorcycle o accelerae o maimum speed from res and is he aerage elociy. Assume hey sar from res.) 1. a = 2 ma acc 2. a = 2 ma 2 d acc correc 3. a = ma acc 4. a = acc. a = d acc 2 acc 6. a = d acc 2 2 acc We are gien he final elociy( ma ), he iniial elociy(rains sar from res), and he displacemen(d acc ). Also we are old ha he acceleraion is consan. We are no old how much ime i akes o reach ma, so i s bes o use a relaion beween elociy, displacemen and consan acceleraion a, hen sole for he acceleraion. 2 = a ( 0 ) 2 ma = a d acc a = 2 ma 2 d acc 008 (par 2 of 3) 3 poins While responding o an emergency hey sar del = 8.6 minues apar. How far ahead is he firs cop when he second one sars? Correc answer: km. This par is asking us how far he firs moorcycle go in del = 8.6 minues. Firs i raeled d acc = 3 km while i was acceleraing, hen i raeled a ma = 279 km/hr for = del acc. So now we need an epression

4 Answer, Key Homework 2 Daid McInyre 4123 Mar 2, for acc. ma = a acc consan? Correc answer: m/s 2. d acc = 1 2 a 2 acc = 1 2 ma acc acc = 2 d acc ma So now he disance he firs moorcycle is ahead, d ahead, when he second moorcycle sars is: d ahead =d acc + ma =d acc + ma ( del acc ) ( =d acc + ma del 2 d ) acc ma =d acc + ma del 2 d acc = ma del d acc =(279 km/hr)(8.6 minues) 1 hr 60 min 3 km = km This makes sense because an objec undergoing uniform acceleraion from res goes half he disance i would go if i were going a is maimum speed during ha ime. 009 (par 3 of 3) 3 poins How far apar are hey when hey are boh raeling a maimum speed? Correc answer: km. nce boh moorcycles are up o full speed hey hae boh spen he same amoun of ime going he same disance while acceleraing so heir disance apar from each oher is simply: d apar = ma del = (279 km/hr)(8.6 minues) 1 hr 60 min = km 010 (par 1 of 3) 4 poins A hockey puck sliding on a frozen lake comes o res afer raeling 284 m. If is iniial elociy is 3 m/s, wha is is acceleraion if ha acceleraion is assumed Gine : 0 = 3 m/s, = 284 m, = 0 m/s. wih = 0 m/s, so a = = a = (3 m/s)2 2(284 m) = m/s 2. and 011 (par 2 of 3) 3 poins How long is i in moion? Correc answer: s. = 0 + a, where again = 0 m/s, so = 0 a = 3 m/s m/s 2 = s. 012 (par 3 of 3) 3 poins Wha is is speed afer raeling 230 m? Correc answer: m/s. so ha 2 = a = (3 m/s) 2 Gien : = 230 m. + 2( m/s 2 )(230 m) = m 2 /s 2, = m/s. 013 (par 1 of 3) 4 poins A cerain auomobile manufacurer claims

5 Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 ha is super-delue spors car will accelerae from res o a speed of 43.6 m/s in 7.99 s. Assume ha he acceleraion of he car is consan. a) Find he acceleraion of he car. Correc answer:.4682 m/s 2. Firs noe ha i = 0 and he elociy of he car afer 7.99 s is f = 43.6 m/s. Because we are gien he iniial and final elociies and he lengh of he ime ineral, we can use Again we can use he relaion (alid only he acceleraion is consan) () = 0 + a, his ime wih 0 = 0, a =.4682 m/s 2, and = 9.9 s = 0 + (.4682 m/s 2 ) (9.9 s) = m/s. f = i + a, o calculae he acceleraion a = f i (43.6 m/s) = (7.99 s) =.4682 m/s 2. In realiy, his is an aerage acceleraion, since i is ery unlikely ha a car acceleraes uniformly. 014 (par 2 of 3) 3 poins b) Find he disance he car raels in he firs 7.99 s. Correc answer: m. Le he origin be a he original posiion of he car, so ha i = 0. Using he equaion f i = 1 2 ( f + i ) (alid only for consan acceleraion!), we find ha = 1 (43.6 m/s) (7.99 s) 2 = m. 01 (par 3 of 3) 3 poins c) Wha is he speed of he car 9.9 s afer i begins is moion, assuming i coninues o accelerae a he same aerage rae? Correc answer: m/s.

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