Does a car speedometfy.w ,he*3n dder measure speed, velocity, or both?

Can an object have a varying spe1w7y udq:bz+7d+pw2 v m x(xkked if its velocity is constant? If yes, give exam(71qmyd bkxwdz+wp:+vk u72 x ples.

When an object moves with cy 2ylml9u g4- )/ywocuonstant velocity, does its average velocity during any time interval differ from its instantanwcyou4yl9u )y2-/ gm leous velocity at any instant?

In drag racing, is it possible for the car with the/gfkr5htdla38g zi6 7 greatest speed crossing the finish line to t53zhgikg lfr7/a68d lose the race? Explain.

If one object has a greater speed than a second8ap(m5/cw rz j(2rldn object, does the first necessarily have a greater accel ( mzd28ra/wrjnc5(lp eration? Explain, using examples.

Compare the acceleration of a motorcycle that accelerates from 80km/h to 90 sqck ud06,)uykm/h with the acceleration of a bicycle that accelerates from rest to s,yq) u0u6kdc10km/h in the same time.

Can an object have a northward velocity and a southward acceleration? Explaingnl19 )0ok)e (lesc uh 8lh0bl.

Can the velocity of an object be negative when itsx up dx7+f0m)4)hlmgb acceleration is positive? What about vumm4gpb7x+ x)f) hl0 dice versa?

Give an example where both the velocity a7pd0x+7guk mjnd acceleration are negative.

Two cars emerge side by side from a tunnel. Car A is traveling 2kzf*fb t07 2 *;rjdf xp0fktpwith a speed of 60km/h and has an acceleration of 40km/h/min . Car B has a speed of 40 km/h and has an acceleration of 60km/h/min . Which car is passing the other as they come out of the tunnel? Expl tppdr ffk0f*07zk2 t *2;fjbxain your reasoning.

Can an object be increasing in speed ae e:j21tduxd *,sxln3 d7(f(ke e/h ugs its acceleration decreases? If so, give an example. If not, explain./nx:s udk x7 d2*jte (deh egfl,eu31(

A baseball player hits a foul ball straight up into the j9- ga an00f xrkzc5y9air. It leaves the bat with a speed of 120km/h . In the absence of air res z5-xnf0 kg9 a0r9yjacistance, how fast will the ball be traveling when the catcher catches it?

As a freely falling object speeds up, what is happeni +s,lu -lxa8tong to its acceleration due to gravity — dox8lls+,- otua es it increase, decrease, or stay the same?

How would you estimate the maxi pwr-b*h+ x7p0zl,l1ih xl dt3mum height you could throw a ball vertically upwar+txhiz pr31l* xdl0pbl,h7-wd? How would you estimate the maximum speed you could give it?

You travel from point A to point B in a car moving at a constant speed v77/r-r.ft jcgb 9jobh8k,il75 pjr aof Then you travel the same distance from point B to another point C, moving at a constant speed of 90km/h . Is your average speed for the entire trip 7 -boihl p58v 97rrb f a7g,rcjt/jjk.from A to C 80km/h ? Explain why or why not.

In a lecture demonstration, a 3.0-m-long vertb7- zh; 0r x4g11c/phroqxlp hical string with ten bolts tied to it at equal intervals is dropped from the ceiling of the lecture hall. The string falls on a tin plate, and the class hears the clink of each bolt as it hits the plate. The sounds will not occur at equal time intervals. Why? Will the time 0r-xh;ohh/pl1c 1p47bqxzr g between clinks increase or decrease near the end of the fall? How could the bolts be tied so that the clinks occur at equal intervals?

Which one of these motions is not at cons5,hqrtuck/w8(e w i*yv 2 rv5jtant acceleration: a rock falling from a cliff, an elevator moving from the j,w/ v25ew c(5ih*rrv 8tukqysecond floor to the fifth floor making stops along the way, a dish resting on a table?

An object that is thrown vertically upward will return to its original pos ci jn(1om0c-.d-ju/n4zp iyjjri62cition with the same spejn6i cm.4 yznupc-jj1 -riioj0( 2/dced as it had initially if air resistance is negligible. If air resistance is appreciable, will this result be altered, and if so, how? [Hint: The acceleration due to air resistance is always in a direction opposite to the motion.]

Can an object have zo/+h.t*,k vx ghzh6pqero velocity and nonzero acceleration at the same time? Give e* .z+,phvkqo ht6ghx /xamples.

Can an object have zero acceleration and nonzero velocity at the same timehh kpam*w;j26 zd: q7j? Give examplesw*:7 hjzd jph6k2;qma .

Describe in words the motion plotted in Fig. id28y,elyy qtk z:q:, 2–28 in terms of v, a, etc. [Hint: First try to duplicate the motion plotydk i::2y8l,ty zqeq ,ted by walking or moving your hand.]

Describe in words the motion of the object grap uty:g9gx6k 57 idcqh.hed in Fig. 2–29.

  What must be your car’u7 n; f-ckoo)ls average speed in order to travel 235 km in 3.25 h?    km/h

  A bird can fly 25 km/h How long does it take to fly 15 kuife./.yxg( b m?    h

  If you are driving along a s h)eew;fx1b1 zu ii.h /cy8ad1u*ze8wtraight road and you look to the side for 2.0 s, how far do you travel during this inattentive period? w1/18ue*f)eh ;hyb ez1xwc8 daz. iiu   m

  Convert 35 mi/h to mqnvo1x- mn sz4eb92qmf 8i(0
(a) km/h,    km/h
(b) m/s ,    m/s
(c) ft/s.    ft/s

  A rolling ball moves f/ha kuml ar6v7utz;d3.zi7:ck 0uua(rom $x_1$ = 3.4 cm to $x_2$ = -4.2 cm during the time from $t_1$ = 3.0 s to $t_2$ = 6.1 s What is its average velocity?    cm/s

  A particle at $t_1$ = -2.0 s is at $x_1$ = 3.4 cm and at $t_2$ = -4.5 s is at $x_2$ = 8.5 cm What is its average velocity? Can you calculate its average speed from these data?    cm/s

  You are driving home from school steadily at 95 km/h for 1z4s 7*fbf0v rg30 km. It then begins to rain and you slow to 65 km/h You0v47bffr g sz* arrive home after driving 3 hours and 20 minutes.
(a) How far is your hometown from school?    km
(b) What was your average speed?    km/h

  According to a rule-of-thumb, every five sd .0:p g*0pttu5blqi veconds between a lightning flash and the following thunder gives the distance to the flash in miles. Assuming that the flasht5vb 0lqdpu:0*t .igp of light arrives in essentially no time at all, estimate the speed of sound in m/s from this rule.    m/s

  A person jogs eight complete laps around a quaki7 h3g 0(sikb6 3xcrkrter-mile track in a total time of 12.5 min6sr ihxgkb kc373(k0 i. Calculate
(a) the average speed    m/s
(b) the average velocity, in    m/s

  A horse canters away from its trainer in a straight line, moving 116 m awayk q h:)lk8y/tr in 14.0 s. It then turns abruptlkl 8y)tkr/q: hy and gallops halfway back in 4.8 s. Calculate
(a) its average speed    m/s
(b) its average velocity for the entire trip, using “away from the trainer” as the positive direction.    m/s

  Two locomotives approach each other on parallel tracks. Each has a speq)g 0ptp5 s)9w4 e en/t:jimbred of 95 km/h with respect to the ground. If they are initially 8.5 km apart, how long will it be before they reach each other? (See Fig. 2–30). pepem) 5g4)rttjs/9b 0niw :q   min

  A car traveling 88 km/h is 110 m behind a truc-jrpnf/ le1y d). +gkdcf)1nrk traveling How long will it take the car to reach the-dc1+d)/jl re1.ng) yrnp ffk truck?    s

  An airplane travels 3100 km at a speed of 79czcrdo26q2lr4 nv6 2l 0 km/h , and then encounters a tailwind that b2d42 2czl n6rv l6rqcooosts its speed to 990 km/h for the next 2800 km.
What was the total time for the trip?    h
What was the average speed of the plane for this trip? [Hint: Think carefully before using Eq. 2–11d.]    km/h

  Calculate the average speed and average velocity of a complete round-trip**3qo v-btk/d wyt32wszo av+ in which the outgoing 250 km is covered at 95 km/h followed by a 1.0-hour w3qz*o/y -kvtvt2ao3w*+db slunch break, and the return 250 km is covered at 55 km/h.    km/h

  A bowling ball traveling with constant speed hits the pin-w axjf)u(xbdf;a3m g)1e9hgs at the end of a bowling lane 16.5 m long. The bowler hears the sound of the ball hittmw-9adbg()jfxehu gf)x1a ;3ing the pins 2.50 s after the ball is released from his hands. What is the speed of the ball? The speed of sound is 340 m/s.    m/s

  A sports car accelerates from re fhi9.a8 ovjrmjm,f4;st to 95 km/h in 6.2 s. What is its average acceleration in 8.hmi,a jffm9v jr;4o$m/s^2$ ?    $m/s^2$

  A sprinter accelerates from rest to 10.0 m/s in fqybx :cn4xc5bp5 j29 1.35 s. What is her acceleration59nbbc2 yxp qc5fj4x:
(a) in $m/s^2$ ,    $m/s^2$
(b) in $km/h^2$ ?    $km/h^2$

  At highway speeds, a particular automobile is capable of z5uqh+ n+vjb:mcm-ey m-2ec7 an acceleration of about y2 nju+ 7:c-vmq5be zcmm-h+ e$1.6 m/s^2$ At this rate, how long does it take to accelerate from 80 km/h to 110 km/h ? $\approx$    s (Round to the nearest integer)

  A sports car moving at constant speed travels 110 m in 5.4ig8q7x:nr00eig n+m iyblz +0 s. If it then brakes and comes to a stop in 4.0 s, what is its accelerati0q8 nr: i++i0 ez7gilgmbyx4n on in $m/s^2$ ? Express the answer in terms of “g’s,” where 1.00 g = 9.80 $m/s^2$ .    $m/s^2$    g's

The position of a racing car, which starts from rest at t = 0 and mj32xqar7fk4 *yx gj(t oves in a straight line, is given as a function of time in the following Table. Estimate (a) its velocity and (b) its acceleration as a j3a* 4rqk(x x7ygftj2function of time. Display each in a Table and on a graph.

  A car accelerates from 1px+o4 xf-nni13 m/s to 25 m/s in 6.0 s. What was its acceleration? How far did it travel in this time? Assume constant acceleration. +p n 4if1nxxo-   $m/s^2$    m

  A car slows down from 23 m/s to rest in a distance of 85 m. W: 6k:m*bkg5fae2 6grv fd ne;ehat was its acceleration, avn*k: eegm;5e f dkf2g 6:rba6ssumed constant?    $m/s^2$

  A light plane must reach ajaacq4l(o6u+; 8jd+ do4 jvb o speed of 33 m/s for takeoff. How long a runway is needed if the (constant) accelerajoqd8vlcuo6 +d ;a4 (4ajj+botion is $3.0 m/s^2$ ?    m

  A world-class sprinter can burst out of the blocks to essentiaw u/ixww7d3 buv(6+lb7 d8 zprlly top speed (of about 11.5 m/s) in the first 15.0 m of the race. What is the average acceleration of this sprinter, and how long does it take her b7(ww6duu7 rxp/l 3z8+v diwbto reach that speed? $\approx$ =    $m/s^2$ (retain two decimal places)    s

  A car slows down uniformly from a speed of2adyr2o 8 pk3a 12.0 m/s to rest in 6.00 s. How far did it travel i2dra8a ok 23ypn that time?    m

  In coming to a stop, a car leaves skid marks 92 tp:v.q:kr yiw0qztyd, p2zam q8 *yr./.o ,eb m long on the highway. Assuming a deceleration of taz vp,oq.pkrq*,8e: d:qz/t y.m yb 2wy.r 0i$7.00 m/s^2$ estimate the speed of the car just before braking.    m/s

  A car traveling 85 km/h strikek) g5o1 3osx, a lvqh*dxdu;t7s a tree. The front end of the car compresses and the driver comes to rest after traveling 0.80 m. What was the average acceleration of thodx5g udhl; )*,vs7ox qt13ake driver during the collisi on? Express the answer in terms of “g’s,” where 1.00 g = 9.8 $m/s^2$ . =    $m/s^2$ (retain two decimal places )    g’s

  Determine the stopping distances for a car with an initial speed of 95 ctb /7cek4d.pkm/h and huma7tk. bpdc4/c en reaction time of 1.0 s, for an acceleration
(a) a = -4.0 $m/s^2$ ;    m
(b) a = -8.0 $m/s^2$    m

Show that the equation for th /gt6w0g 6;kzr0;(bp d1ftcm z9poae we stopping distance of a car is $d_S\,=\,v_0t_R\,-\,{v_0}^2/(2a)$ , where $ v_0$ is the initial speed of the car, $ t_R $ is the driver’s reaction time, and a is the constant acceleration (and is negative).

A car is behind a truck going 25 m/s on1p biras2dy64y**oto the highway. The car’s driver looks for an opportunity to pass, guessing that his car can acbsi 1y*poayo d6r 2*t4celerate at 1.0 $m/s^2$ He gauges that he has to cover the 20-m length of the truck, plus 10 m clear room at the rear of the truck and 10 m more at the front of it. In the oncoming lane, he sees a car approaching, probably also traveling at 25 m/s He estimates that the car is about 400 m away. Should he attempt the pass? Give details.

A runner hopes to complete the 10,000-m run in7n(rs.nikijz w i-* t, less than 30.0 min. After exactly 27.0 min, there are still 1100 m to go. The runner must thei7-k.jnnz,rs (wt i*in accelerate at 0.20 $m/s^2$ for how many seconds in order to achieve the desired time?

A person driving her car at 45 km/h approaches an intersection jusj s2u.k8 e4fbdo w1r1ai9-gg ht as the traffic light turns yellow. She knows that the yellow light lasts only 2.0 s before turning red, and she is 28 m away from the near side of the intersection (Fig. 2–31). Should she try to stop, or should she speed up to cross the intersection before the light turnk8. ir wuh1dogfab -s g429ej1s red? The intersection is 15 m wide. Her car’s maximum deceleration is $-5.8 m/s^2$ , whereas it can accelerate from 45 km/h to 65 km/h in 6.0 s. Ignore the length of her car and her reaction time.

  A stone is dropped from the top of a cliff. It hits the ground below after 3.2 l.w ipbc(lh-gd q,; c+s*naf45 s. Hofl cp sq+c 4 d,h.-l;(nbawi*gw high is the cliff?    m

  If a car rolls gentlt( 889 paw: lw1bzc7wo(hjo3f xtjf2 )dtui;uy ($v_0\,=\,0$) off a vertical cliff, how long does it take it to reach 85 km/h ?    s

  Estimate
(a) how long it took King Kong to fall straight down from the top of the Empire State Building (380 m high), $\approx$ =    s (retain one decimal places)
(b) his velocity just before “landing”?    m/s

  A baseball is hit nearly straight up into the air with a gq3f jie :s,omq)y8o2speed of 22 m/s
(a) How high does it go?    m
(b) How long is it in the air?    s

  A ballplayer catches a ball 3.0 s after t7qh ylu-w/ef ud /y:p:hrowing it vertically upward. With what speed did he t- eu:/:hu/y q lfypwd7hrow it, and what height did it reach?    m/s (Round to the nearest integer)    m

An object starts from rest and falls under the influence of gravity. Dn 0-wyb,5+ jn 6iwyhrrn96gazraw graphs of (a) its speed and (b) the distance it has fallen, as a function of time from t = 0 to t = 5.00 s . Ignore air resistanc, 96-n6wy 0nb5gzjhinarr +ywe.

A helicopter is ascending vertically with a speed of 5.20 m/s. At ad t xu ztny )pz*5zz9j*b(8ym+ height of 125 m above the Earth, a package is dropped from a window. How much time does it take for the packagez up+zx *ym nb8*)jdt9(zt5zy to reach the ground? [Hint: The package’s initial speed equals the helicopter’s.] t =__ s

For an object falling freely from rest, show that the distance traveled fk t8v 1:ipr:gduring each successive second increases in the ratio of successive odd integers (1, 3, 5, etc.). This was first shown by Galileo. See Figs.pi81 gtk:fvr : 2–18 and 2–21.

If air resistance is neglected, show (algebre+wib ;p16q:cltu r8xaically) that a ball thrown vertically upward wr:1 ubt + ;plqe8cx6iwith a speed $v_0$ will have the same speed, $v_0$, when it comes back down to the starting point.

  A stone is thrown vertically u-rs- ddiddt a4/2 ) tlvxsnd.y(60gljpward with a speed of 18.0 m/s
(a) How fast is it moving when it reaches a height of 11.0 m? |v| =    m/s
(b) How long is required to reach this height? t =    s,    s
(c) Why are there two answers to (b)?

  Estimate the time between each photoflash of the app 9mz1nynr9gl(le in Fig. 2–18 (or number of photoflashes per second). Assume the apple is about 10 cm in diameter. [Hint: Use two apple positions, but not the unclear n mnl1 9gy(r9zones at the top.]
T =    s
   flashes per second

  A falling stone takes 0.28 s to travel past a window 2.2 m tall (Fig r vn ;rvnpnvu,u2;;;:qfefl:. 2–32). From what height above the top o; vvf;:reu nf,;n n2ur:;vl pqf the window did the stone fall?    m

  A rock is dropped from a sea cliff, and the sound of it s+xd3jzxa) zm9 triking the ocean is heard 3.2 s later. If the speed of sound is 340 m/s , how higd z3+zx9jmxa)h is the cliff? H =    m

  Suppose you adjust your garden hose nozzle for a hard stream of v (zmx/e bm hi0fqea7(b4/)p hwater. You point the nozzle vertically upward at a height of 1.5 m above the ground (Fig. 2–33). When you quickly move the nozzle away from the vertical, you hpef/b( v bh)e4/7aq( ix0mzhmear the water striking the ground next to you for another 2.0 s. What is the water speed as it leaves the nozzle?    m/s

  A stone is thrown ve1 py:tn- :wmxsrtically upward with a speed of 12.0 m/s from the edge of a ct::pmsw1xyn - liff 70.0 m high (Fig. 2–34).
(a) How much later does it reach the bottom of the cliff? t =    s
(b) What is its speed just before hitting?    m/s
(c) What total distance did it travel?    m

  A baseball is seen to pass upwar r356nj9 cjtgnd by a window 28 m above the street with a vertical speed of 13 m/s If the ball was t5 nrnj9g36 ctjhrown from the street,
(a) what was its initial speed,    m/s
(b) what altitude does it reach,    m
(c) when was it thrown,    s
(d) when does it reach the street again?    s

Figure 2–29 shows the velocity of a04-a -6zgwguylm;jd 9m vji ;6-g8vaxo )wxwh train as a function of time. (a) At what time was its velocity greatest? (b) During what periods, if any, was the velocity constwdgx; uwvvxa)jzm 0go6;j--9 4-g ial wyh6 m8ant? (c) During what periods, if any, was the acceleration constant? (d) When was the magnitude of the acceleration greatest?

  The position of a rabbit along a straight tunnel as a function t7;xyeio lgsr9ph5 e: i-94jp of time is plotted in Fig. 2–28. What is itepo -99ii;jtg hxl psy:57 re4s instantaneous velocity
(a) at t = 10.0 s    m/
(b) at t = 30.0 s What is its average velocity    m/s
(c) between t = 0 and t = 5.0 s    m/s
(d) between t = 25.0 s and t = 30.0 s    m/s
(e) between t = 40.0 s and t = 50.0 s ?    m/s

  In Fig. 2–28,
(a) during what time periods, if any, is the velocity constant? t =    s to t $\approx$    s
(b) At what time is the velocity greatest? t =    s
(c) At what time, if any, is the velocity zero? t =    s
(d) Does the object move in one direction or in both directions during the time shown?

  A certain type of automobile can accelerate approximately as r9tsg1.8 stbai 9wnot 6mjl/ )shown in the velocity– nl8/1aw9sj6t).bro9 itsm gttime graph of Fig. 2–35. (The short flat spots in the curve represent shifting of the gears.)
(a) Estimate the average acceleration of the car in second gear and in fourth gear. The average acceleration in $2^{nd}$ gear is given by    $m/s^2$ The average acceleration in $4^{th}$ gear is given by    $m/s^2$
(b) Estimate how far the car traveled while in fourth gear.    m

  Estimate the average acceleration of t0zgk te- kht1* bg du2hhf:*9the car in the previous Problem (Fig. 2–35) when it is hb2f-tz *g0:*khh1t dk9gteu in
(a) first,    $m/s^2$
(b) third,    $m/s^2$
(c) fifth gear.    $m/s^2$
(d) What is its average acceleration through the first four gears?    $m/s^2$

  In Fig. 2–29, estimate the dise ntoq3g/ 4nj-tance the object traveled during
(a) the first minute,   
(b) the second minute.    m

Construct the vs. t gra:ur( qhn m ph7vbr0(x3ph for the object whose displacement as a function of time is given by Fvh(:qhmubxn (rpr3 07ig. 2–28.

Figure 2–36 is a position versus time graph for the motiocuh 3(li it6j4j1dppo,c(3u xn of an object along the x axis. Consider the time interval from A to B. (a) Is the object moving in the positive or negative direction? (b) Is the object speeding up or slowing down? (c) Is the acceleration of the object positive or negative? Now consider the time interval from D to E. (d) Is the object moving in the pot(u433h d(u6jic pi,p xcj1lositive or negative direction? (e) Is the object speeding up or slowing down? (f) Is the acceleration of the object positive or negative? (g) Finally, answer these same three questions for the time interval from C to D.

  A person jumps from a f+d yn;6 ang ,urgd5ss1vj5lo9ourth-story window 15.0 m above a firefighter’s safety net. The survivor stretches the net 1.0 m before sn 95 gyo61 +5la;vjs nddu,grcoming to rest, Fig. 2–37.
(a) What was the average deceleration experienced by the survivor when she was slowed to rest by the net?    $m/s^2$
(b) What would you do to make it “safer” (that is, to generate a smaller deceleration): would you stiffen or loosen the net? Explain.  ----待选择----stiffen loosen 

The acceleration due to gravity on the Moon is about one-sixth what it is uy)14 zx 6gyjvon Earth. If an object is thrown vertically upward on the Moon, how many times higher will it go than it would on Earth, assuming the same initial veloj41xvzu6 gy)ycity?

  A person who is properly constrained by an over-the-shoulde4)aas.y hzl(e6alypfyhl h,obq8so 93 ;2gq8r seat belt has a good chance of surviveq a8 l2fhsqs ol;9h8.g 34plyho z( b6yy),aaing a car collision if the deceleration does not exceed about 30 “g’s” $(1.0 g\,=\,9.8\,m/s^2)$. Assuming uniform deceleration of this value, calculate the distance over which the front end of the car must be designed to collapse if a crash brings the car to rest from 100 km/h . $\approx$    m(retain one decimal places)

  Agent Bond is standing on a bridge, 12 m above the road below, and his pursuers wj zi7 ryi7wym) ,)b8l*g sbh:rq2g2mare getting too close for comfort. He spots a flatbed truck approaching at 25 m/s , which he measures by knowing that the telephone poles the truck is ,qyw hsrbi)g*ilb:m7 2jgzr8y7m 2)wpassing are 25 m apart in this country. The bed of the truck is 1.5 m above the road, and Bond quickly calculates how many poles away the truck should be when he jumps down from the bridge onto the truck to make his getaway. How many poles is it?    poles

  Suppose a car manufacturer tested its cars for front-end collis;- ozgjo3c2z r dk4mb/ nhl8s)ions by hauling them up on a crane and drl3kz h g/o8m2j4sz;)n crobd-opping them from a certain height.
(a) Show that the speed just before a car hits the ground, after falling from rest a vertical distance H, is given by $\sqrt{2gH}$ . What height corresponds to a collision at
(b) 60 km/h ? $\approx$    m (Round to the nearest integer)
(c) 100 km/h ? $\approx$    m (Round to the nearest integer)

  Every year the Earth travels rmls89m g 7e2oabout $10^9\,km$ as it orbits the Sun. What is Earth’s average speed in km/h?    $ \times10^{ 5}\,km/h $

  A 95-m-long train begins uniform acya7rwvtph8 1 9y.5y:rc; ta yyceleration from rest. The front of the train has a speed of 25 m/s when it passes a railway worker who is standing 180 m from where the front of the train started. What will be tv1.wy;8t a7t c ryayyp5y:r 9hhe speed of the last car as it passes the worker? (See Fig. 2–38.)    m/s

  A person jumps off a diving board 4.0 k4*1qf 9g z 17jkpdsnryx9kl;m above the water’s surface into a deep pool. The person’s downward motion stops 2.0 m below the surface of the water. Estimate the aver1lp791d k9g*4zkns qxy;j frkage deceleration of the person while under the water. $\approx$    $m/s^2$ (Round to the nearest integer)

  In the design of a rapid transit system, it is necessary to balance zohl )d +3/ukathe average speed of a train against the distu+alho)3d/ k zance between stops. The more stops there are, the slower the train’s average speed. To get an idea of this problem, calculate the time it takes a train to make a 9.0-km trip in two situations:
(a) the stations at which the trains must stop are 1.8 km apart (a total of 6 stations, including those at ends);    min
(b) the stations are 3.0 km apart (4 stations total). Assume that at each station the train accelerates at a rate of $1.1 m/s^2$ until it reaches 90 km/h then stays at this speed until its brakes are applied for arrival at the next station, at which time it decelerates at $-2.0 m/s^2$ Assume it stops at each intermediate station for 20 s.    min

  Pelicans tuck their wingsd dc;5 yxbq-j4 and free fall straight down when diving for fish. Suppose a pelican starts its dive from a height of 16.0 m an 5ydqj-bxcd4 ;d cannot change its path once committed. If it takes a fish 0.20 s to perform evasive action, at what minimum height must it spot the pelican to escape? Assume the fish is at the surface of the water.    m

  In putting, the force with whivjppr g7q o2:eu4yq (3ch a golfer strikes a ball is planned so that the ball will stop within some sm:qqj yuo3pr( 2v74 egpall distance of the cup, say, 1.0 m long or short, in case the putt is missed. Accomplishing this from an uphill lie (that is, putting downhill, see Fig. 2–39) is more difficult than from a downhill lie. To see why, assume that on a particular green the ball decelerates constantly at $20 m/s^2$ going downhill, and constantly at $3.0 m/s^2$ going uphill. Suppose we have an uphill lie 7.0 m from the cup. Calculate the allowable range of initial velocities we may impart to the ball so that it stops in the range 1.0 m short to 1.0 m long of the cup.    m/s to    m/sDo the same for a downhill lie 7.0 m from the cup.    m/s to    m/sWhat in your results suggests that the downhill putt is more difficult?

  A fugitive tries to hop on a freiyq6 j(t 9/0txq me4dnou8u6 zjght train traveling at a constant speed of 6.0 m/s6j9t8o/ed 04q mzyxuq (tu j6n Just as an empty box car passes him, the fugitive starts from rest and accelerates at $a\,=\,4.0 m/s^2$ to his maximum speed of 8.0 m/s
(a) How long does it take him to catch up to the empty box car?    s
(b) What is the distance traveled to reach the box car?    m

  A stone is dropped from the roof of a high building. A second stone ok,, -q3i9mpp z5j kekis dropped 1.50 s l-9ojpk,zek pi,q 5 3kmater. How far apart are the stones when the second one has reached a speed of 12.0 m/s ?    m

  A race car driver must average 200.0 km/h over the course of a time jn)22 le1j5pp+jzmsvtrial lasting ten laps. If the first nisp)m1 e+p2jv25 nljz jne laps were done at 198.0 km/h . what average speed must be maintained for the last lap?    km/h

  A bicyclist in the Tour de Frdxqx6 :74tyd oance crests a mountain pass as he moves at 18 km/h . oxyd:qt 67d4x At the bottom, 4.0 km farther, his speed is 75 km/h . What was his average acceleration (in $m/s^2$) while riding down the mountain?    $m/s^2$

  Two children are playing on two tramm ys) e(bud,n8polines. The first child can bounce up one-and-a-half times higher than the second child. The inieu y 8b)m,(sndtial speed up of the second child is $5.0 m/s $.
(a) Find the maximum height the second child reaches. $\approx$    m(retain one decimal places)
(b) What is the initial speed of the first child? $\approx$    m/s(retain one decimal places)
(c) How long was the first child in the air?    s

  An automobile traveling 95 km/h overtakes a 1.10-km-locinl9x-oj .bk xv xz1*7)7ck2jtlkt/9z f kc:ng train traveling in the same direction on a track parallel to the road. If the train’s speed is 75 km/h . how long does it take the car to pass it, and how far will the car have traveled in this time? See Fig. 2–40. What are the results if the car and train are traveling in opposite directi*i9l ck9v17: /obx-jct2xkjf tnk )klx7z zc.ons? t =    min The distance the car travels during this time is $\approx$    km(retain one decimal places) t =    min The distance the car travels during this time is $\approx$    km(retain one decimal places)

  A baseball pitcher throws a baseball with a speed of 44 m/s In thrtd47wrd4 ui8u6 g-uwcowing the baseball, the pitcher accelerates the ball through a displacement of about 3.5 m, from behind the body to the point where it is releaseduu-ug67ctd ir8wd44w (Fig. 2–41). Estimate the average acceleration of the ball during the throwing motion.    $m/s^2$

  A rocket rises vertically, from 1n5k(/ b)xs)jjm fhuzh3xss1 rest, with an acceleration of $3.2 m/s^2$ until it runs out of fuel at an altitude of 1200 m. After this point, its acceleration is that of gravity, downward.
(a) What is the velocity of the rocket when it runs out of fuel? $\approx$ =    m/s(Round to the nearest integer)
(b) How long does it take to reach this point? $\approx$ =    s(Round to the nearest integer)
(c) What maximum altitude does the rocket reach?    m
(d) How much time (total) does it take to reach maximum altitude? $\approx$ =    s(Round to the nearest integer)
(e) With what velocity does the rocket strike the Earth?    m/s
(f) How long (total) is it in the air?    s

  Consider the street pattern shown inu1pf+tuf .*:p d+cem y Fig. 2–42. Each intersection has a traffic signal, and the speed limit is 50 km/s . Suppose you are drivingct+m. euy *1up+f:pfd from the west at the speed limit. When you are 10 m from the first intersection, all the lights turn green. The lights are green for 13 s each.
(a) Calculate the time needed to reach the third stoplight. Can you make it through all three lights without stopping?  ----待选择----yesno 
(b) Another car was stopped at the first light when all the lights turned green. It can accelerate at the rate of $2.0 m/s^2$ to the speed limit. Can the second car make it through all three lights without stopping?  ----待选择----yesno 

  A police car at rest, passed by a speeder ibt sj* 5/t(gtrv03 6pq5uqkxtraveling at a constant 120 km/h takes off in hotr 3xgq6bu0/*5 pqtvti s ktj(5 pursuit. The police officer catches up to the speeder in 750 m, maintaining a constant acceleration.
(a) Qualitatively plot the position vs. time graph for both cars from the police car’s start to the catch-up point. Calculate
(b) how long it took the police officer to overtake the speeder, $\approx$ =    s(Round to the nearest integer)
(c) the required police car acceleration, $\approx$ =    $m/s^2$(Round to the nearest integer)
(d) the speed of the police car at the overtaking point. $\approx$ =    m/s(Round to the nearest integer)

  A stone is dropped from the roof of a building; 2.00 s after that, a r uonnr0 e6;/usecond stone is thrown straight down with an initial speed of 25.0 m/s and the two stones land at the same time.orur ;6nn/ue0
(a) How long did it take the first stone to reach the ground? $t_1$ =    s
(b) How high is the building?    m
(c) What are the speeds of the two stones just before they hit the ground? #1    m/s #2    m/s

  Two stones are thrown vertically up adx9z:g9 d xanfjsd9:7t the same time. The first stone is thrown with an initial velocity of 11.0 m/s from a 12th-floor balcony of a building and hits the ground after 4.5 s. With what initial velocity shos:x da799dfg n :dj9zxuld the second stone be thrown from a $4^{th}$-floor balcony so that it hits the ground at the same time as the first stone? Make simple assumptions, like equal-height floors.    m/s

  If there were no air resistance, how long would it take a free-fall+ e+,mrblz0j+o+ s;bruck3o cing parachutist to fall f3j0 c+burk lcmorb++s z ,;eo+rom a plane at 3200 m to an altitude of 350 m, where she will pull her ripcord? What would her speed be at 350 m? (In reality, the air resistance will restrict her speed to perhaps 150 km/h .)
   s
   km/h

  A fast-food restaurant uses a conveyor belt s61e;0ckzo3oztf cc ) to send the burgers through a grilling machine. If the grilling machine is 1.1 m long and the burgers require 2.5 min to cook, how fast must the conveyor belt travel? If the burger ; e3oc) 0ftszkzc16cos are spaced 15 cm apart, what is the rate of burger production (in burgers/min)?
   m/min
   $\frac{burgers}{min}$

  Bill can throw a ballhiv n-gt*h2j98iv c 0jew s +9lyi*y8a vertically at a speed 1.5 times faster than Joe can. How many times higher will Bill’s ba *-jih8+0lg9 i 8htj2eyyvcvi 9an w*sll go than Joe’s? $\approx$ =    (retain one decimal places)

  You stand at the top of a cliff while your friend stands on the k) 8e+7 ojms,t qypdr7 c4es*oground below you. You drop a ball from rest and see that it takes 1.2 pt ,js7sqe7*e8)o+d 4c romyks for the ball to hit the ground below. Your friend then picks up the ball and throws it up to you, such that it just comes to rest in your hand. What is the speed with which your friend threw the ball?    m/s

  Two students are asked to find t 73oq jnwj h/1uu04kqthe height of a particular building using a barometer. Instead of using the barometer as an altitude-measuring device, they take it to the roof of the building and drop it off, timing its fall. One student reports a fall time of 2.0 s, and the other, 2.3 s. How much difference does the 0.3 s make for the estimates of the building’s n j/ qu4ot0k 71u3wjqhheight?    m

Figure 2–43 shows the position vs. time graph for two bicycles, A and B.eyfoa3y hm1q9 t y31:7(aqae6amy eo. (a) Is there any instant at which the two bicycles have the same velocity? (b) Which bicycle has the larger acceleration? (c) At which instant(s) are the bicycles passing each other? Which bicycle is passing the other? (d) Which bicycle has the highest instantaneous velocity? (e) Whi:y 9hoa.31foa et13( 6emya qy yeaq7mch bicycle has the higher average velocity?