Chapter 2 2 Avar 5055 Train Starts From Rest And

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20) A motorist makes a trip of 180 miles. For the first 90 miles she drives at a constant speed of

30 mph. At what constant speed must she drive the remaining distance if her average speed for

the total trip is to be 40 mph?

A) 45 mph

B) 50 mph

C) 52.5 mph

D) 55 mph

E) 60 mph

21) Human reaction times are worsened by alcohol. How much further (in feet) would a drunk

driver’s car travel before he hits the brakes than a sober driver’s car? Assume that both are

initially traveling at 50.0 mi/h and their cars have the same acceleration while slowing down, and

that the sober driver takes 0.33 s to hit the brakes in a crisis, while the drunk driver takes 1.0 s to

do so. (5280 ft = 1 mi)

22) Arthur and Betty start walking toward each other when they are 100 m apart. Arthur has a

speed of 3.0 m/s and Betty has a speed of 2.0 m/s. How long does it take for them to meet?

23) The position x(t) of a particle as a function of time t is given by the equation x(t) = (3.5 m/s)t

– (5.0 m/s2)t2. What is the average velocity of the particle between t = 0.30 s and t = 0.40 s?

24) A water rocket can reach a speed of 75 m/s in 0.050 seconds from launch. What is its

average acceleration?

25) An airplane increases its speed at the average rate of 15 m/s2. How much time does it take

to increase its speed from 100 m/s to 160 m/s?

A) 17 s

B) 0.058 s

C) 4.0 s

D) 0.25 s

26) The captain orders his starship to accelerate from rest at a rate of “1 g” (1 g = 9.8 m/s2).

How many days does it take the starship to reach 10% the speed of light? (Light travels at 3.0 ×

108 m/s.)

27) A car is traveling north at After 12 s its velocity is in the same direction.

Find the magnitude and direction of the car’s average acceleration.

A) 0.30 m/s2, south

B) 2.7 m/s2, south

C) 0.30 m/s2, north

D) 2.7 m/s2, north

28) A racquetball strikes a wall with a speed of 30 m/s and rebounds in the opposite direction

with a speed of 26 m/s. The collision takes 20 ms. What is the average acceleration of the ball

during the collision with the wall?

A) 0 m/s2

B) 200 m/s2

C) 2800 m/s2

D) 1500 m/s2

E) 1300 m/s2

29) The velocity v(t) of a particle as a function of time is given by v(t) = (2.3 m/s) + (4.1 m/s2)t –

(6.2 m/s3)t2. What is the average acceleration of the particle between t = 1.0 s and t = 2.0 s?

A) -13 m/s2

B) -15 m/s2

C) 13 m/s2

D) 15 m/s2

E) 0 m/s2

30) If a car accelerates at a uniform 4.0 m/s2, how long will it take to reach a speed of 80 km/hr,

starting from rest?

31) A car that is initially moving at 7.50 m/s begins to accelerate forward uniformly at 0.550

m/s2.

(a) How long after beginning to accelerate does it take the car to move 3.50 km?

(b) How fast is the car moving just as it has traveled 3.50 km?

32) An auto accelerates forward from 7.0 m/s at a uniform 0.71 m/s2. It travels a distance of

1.033 km while accelerating.

(a) How fast is the auto moving just as it is traveled the 1.033 km?

(b) How many seconds did it take to travel the 1.033 km?

33) In a ballistics test, a bullet moving horizontally with a speed of 500 m/s strikes a sandbag and

penetrates a distance of 10.0 cm.

(a) What is the magnitude of the average acceleration of the bullet in the sandbag?

(b) How many milliseconds does it take the bullet to come to rest in the sandbag?

34) A certain test car can go from rest to 32.0 m/s in 3.88 s. The same car can come to a full stop

from that speed in 4.14 s. What is the ratio of the magnitude of the starting acceleration to the

stopping acceleration?

A) 0.937

B) 1.07

C) 0.878

D) 1.14

35) A car initially traveling at 60 km/h accelerates at a constant rate of 2.0 m/s2. How much

time is required for the car to reach a speed of 90 km/h?

A) 15 s

B) 30 s

C) 45 s

D) 4.2 s

36) A cart starts from rest and accelerates uniformly at 4.0 m/s2 for 5.0 s. It next maintains the

velocity it has reached for 10 s. Then it slows down at a steady rate of 2.0 m/s2 for 4.0 s. What

is the final speed of the car?

A) 20 m/s

B) 16 m/s

C) 12 m/s

D) 10 m/s

37) A car travels at 15 m/s for 10 s. It then speeds up with a constant acceleration of 2.0 m/s2 for

15 s. At the end of this time, what is its velocity?

A) 15 m/s

B) 30 m/s

C) 45 m/s

D) 375 m/s

38) A cart with an initial velocity of 5.0 m/s to the right experiences a constant acceleration of

2.0 m/s2 to the right. What is the cart’s displacement during the first 6.0 s of this motion?

A) 10 m

B) 55 m

C) 66 m

D) 80 m

39) A jet plane is launched from a catapult on an aircraft carrier. In 2.0 s it reaches a speed of 42

m/s at the end of the catapult. Assuming the acceleration is constant, how far did it travel during

those 2.0 s?

A) 16 m

B) 24 m

C) 42 m

D) 84 m

40) A car starting from rest accelerates at a constant 2.0 m/s2 for 10 s. It then travels with

constant speed it has achieved for another 10 s. Then it finally slows to a stop with constant

acceleration of magnitude 2.0 m/s2. How far does it travel after starting?

A) 200 m

B) 300 m

C) 400 m

D) 500 m

41) A car increases its forward velocity uniformly from 40 m/s to 80 m/s while traveling a

distance of 200 m. What is its acceleration during this time?

A) 8.0 m/s2

B) 9.6 m/s2

C) 12 m/s2

D) 24 m/s2

42) An object starts from rest and undergoes uniform acceleration. During the first second it

travels 5.0 m. How far will it travel during the third second?

A) 5.0 m

B) 15 m

C) 25 m

D) 45 m

43) An object is moving in a straight line with constant acceleration. Initially it is traveling at 16

m/s. Three seconds later it is traveling at 10 m/s. How far does it move during this time?

A) 30 m

B) 39 m

C) 48 m

D) 57 m

44) A car starts from rest and accelerates uniformly at 3.0 m/s2 toward the north. A second car

starts from rest 6.0 s later at the same point and accelerates uniformly at 5.0 m/s2 toward the

north. How long after the second car starts does it overtake the first car?

A) 12 s

B) 19 s

C) 21 s

D) 24 s

45) A car with good tires on a dry road can decelerate (slow down) at a steady rate of about 5.0

m/s2 when braking. If a car is initially traveling at 55 mi/h

(a) how much time does it take the car to stop?

(b) what is its stopping distance?

46) At the instant a traffic light turns green, a car that has been waiting at the intersection starts

ahead with a constant acceleration of 2.00 m/s2. At that moment a truck traveling with a

constant velocity of 15.0 m/s overtakes and passes the car.

(a) Calculate the time necessary for the car to reach the truck.

(b) Calculate the distance beyond the traffic light that the car will pass the truck.

47) Starting from rest, a dragster travels a straight 1/4 mi racetrack in 6.70 s with constant

acceleration. What is its velocity when it crosses the finish line?

A) 269 mi/h

B) 188 mi/h

C) 296 mi/h

D) 135 mi/h

48) A bicyclist starts a timed race at In order to win, he must average Assuming

constant acceleration from the start, how fast must he be traveling at the end of the race?

A) 36 mi/h

B) 30 mi/h

C) 24 mi/h

D) 42 mi/h

49) A car accelerates from to at a constant rate of How far does it travel

while accelerating?

A) 69 m

B) 207 m

C) 41 m

D) 117 m

50) An airplane needs to reach a forward velocity of to take off. On a runway,

what is the minimum uniform acceleration necessary for the plane to take flight if it starts from

rest?

A) 0.79 m/s2

B) 0.87 m/s2

C) 0.95 m/s2

D) 1.0 m/s2

51) Assuming equal rates of uniform acceleration in both cases, how much further would you

travel if braking from to rest than from ?

A) 4 times farther

B) 3.2 times farther

C) 4.8 times farther

D) 5.2 times farther

52) Acceleration is sometimes expressed in multiples of g, where is the acceleration

of an object due to the earth’s gravity. In a car crash, the car’s forward velocity may go from

to in How many g‘s are experienced, on average, by the driver?

A) 20 g

B) 14 g

C) 24 g

D) 26 g

53) A baseball is hit with a bat and, as a result, its direction is completely reversed and its speed

is doubled. If the actual contact with the bat lasts 0.45 s, what is the ratio of the magnitude of the

average acceleration of the ball to its original speed?

A) 6.7 s-1

B) 4.4 s-1

C) 2.2 s-1

D) 0.15 s-1

54) A train starts from rest and accelerates uniformly until it has traveled 5.6 km and acquired a

forward velocity of The train then moves at a constant velocity of for 420 s. The

train then slows down uniformly at until it is brought to a halt. The acceleration during

the first 5.6 km of travel is closest to which of the following?

A) 0.16 m/

B) 0.14 m/

C) 0.17 m/

D) 0.19 m/

E) 0.20 m/

55) A train starts from rest and accelerates uniformly until it has traveled 2.1 km and acquired a

forward velocity of The train then moves at a constant velocity of for 400 s. The

train then slows down uniformly at until it is brought to a halt. The distance traveled

by the train while slowing down is closest to

A) 4.4 km.

B) 4.2 km.

C) 4.0 km.

D) 3.8 km.

E) 3.6 km.

56) A soccer ball is released from rest at the top of a grassy incline. After 6.4 seconds the ball

has rolled 91 m with constant acceleration, and 1.0 s later it reaches the bottom of the incline.

(a) What was the ball’s acceleration?

(b) How long was the incline?

57) A car starts from rest and accelerates at a steady 6.00 m/s2. How far does it travel in the first

3.00 s?

A) 9.00 m

B) 18.0 m

C) 27.0 m

D) 36.0 m

E) 54.0 m

58) A car is moving with a constant acceleration. At time t = 5.0 s its velocity is 8.0 m/s in the

forward direction, and at time t = 8.0 s its velocity is 12.0 m/s forward. What is the distance

traveled in that interval of time?

A) 10 m

B) 20 m

C) 30 m

D) 40 m

E) 50 m

59) An airplane starts from rest and accelerates at a constant 10.8 m/s2. What is its speed at the

end of a 400 m-long runway?

A) 37.0 m/s

B) 93.0 m/s

C) 65.7 m/s

D) 4320 m/s

E) 186 m/s

60) A car is moving with a speed of 32.0 m/s. The driver sees an accident ahead and slams on the

brakes, causing the car to slow down with a uniform acceleration of magnitude 3.50 m/s2. How

far does the car travel after the driver put on the brakes until it comes to a stop?

A) 4.57 m

B) 9.14 m

C) 112 m

D) 146 m

E) 292 m

61) A car is traveling with a constant speed when the driver suddenly applies the brakes, causing

the car to slow down with a constant acceleration of magnitude 3.50 m/s2. If the car comes to a

stop in a distance of 30.0 m, what was the car’s original speed?

A) 10.2 m/s

B) 14.5 m/s

C) 105 m/s

D) 210 m/s

E) 315 m/s

62) A car is traveling with a constant speed of 30.0 m/s when the driver suddenly applies the

brakes, causing the car to slow down with a constant acceleration. The car comes to a stop in a

distance of 120 m. What was the acceleration of the car as it slowed down?

A) 3.75 m/s2

B) 4.00 m/s2

C) 4.25 m/s2

D) 4.50 m/s2

E) 4.75 m/s2

63) A car is traveling at 26.0 m/s when the driver suddenly applies the brakes, causing the car to

slow down with constant acceleration. The car comes to a stop in a distance of 120 m. How fast

was the car moving when it was 60.0 m past the point where the brakes were applied?

A) 22.5 m/s

B) 18.4 m/s

C) 15.0 m/s

D) 12.1 m/s

E) 9.20 m/s

64) Car A is traveling at 22.0 m/s and car B at 29.0 m/s. Car A is 300 m behind car B when the

driver of car A accelerates his car with a uniform forward acceleration of 2.40 m/ . How long

after car A begins to accelerate does it take car A to overtake car B?

A) 5.50 s

B) 12.6 s

C) 19.0 s

D) 316 s

E) Car A never overtakes car B.

65) A stone is thrown with an initial upward velocity of 7.0 m/s and experiences negligible air

resistance. If we take upward as the positive direction, what is the velocity of the stone after 0.50

A) 2.1 m/s

B) 4.9 m/s

C) -2.1 m/s

D) -4.9 m/s

E) 0.00 m/s

66) An astronaut on a strange new planet having no atmosphere finds that she can jump up to a

maximum height of 27 m when her initial upward speed is 6.0 m/s. What is the magnitude of the

acceleration due to gravity on the planet?

67) A laser is thrown upward with a speed of 12 m/s on the surface of planet X where the

acceleration due to gravity is 1.5 m/s2 and there is no atmosphere. What is the maximum height

reached by the laser?

A) 8.0 m

B) 18 m

C) 48 m

D) 144 m

68) A laser is thrown upward with a speed of 12 m/s on the surface of planet X where the

acceleration due to gravity is 1.5 m/s2 and there is no atmosphere. How long does it take for the

laser to reach the maximum height?

A) 8.0 s

B) 11 s

C) 14 s

D) 16 s

69) An instrument is thrown upward with a speed of 15 m/s on the surface of planet X where the

acceleration due to gravity is 2.5 m/s2 and there is no atmosphere. How long does it take for the

instrument to return to where it was thrown?

A) 6.0 s

B) 8.0 s

C) 10 s

D) 12 s

70) A hammer is thrown upward with a speed of 14 m/s on the surface of planet X where the

acceleration due to gravity is 3.5 m/s2 and there is no atmosphere. What is the speed of the

hammer after 8.0 s?

A) 7.0 m/s

B) 14 m/s

C) 21 m/s

D) 64 m/s

71) Human reaction time is usually greater than 0.10 s. If your friend holds a ruler between your

fingers and releases it without warning, how far can you expect the ruler to fall before you catch

it, assuming negligible air resistance?

A) At least 3.0 cm

B) At least 4.9 cm

C) At least 6.8 cm

D) At least 9.8 cm

72) A ball is thrown upward at a velocity of 19.6 m/s. What is its velocity after 3.0 s, assuming

negligible air resistance?

A) 9.8 m/s upward

B) 9.8 m/s downward

C) 0 m/s

D) 19.6 m/s downward

73) A bullet shot straight up returns to its starting point in 10 s. What is the initial speed of the

bullet, assuming negligible air resistance?

A) 9.8 m/s

B) 25 m/s

C) 49 m/s

D) 98 m/s

74) A ball is thrown straight up with a speed of 36 m/s. How long does it take to return to its

starting point, assuming negligible air resistance?

A) 3.7 s

B) 7.3 s

C) 11 s

D) 15 s

75) A ball is thrown downward from the top of a building with an initial speed of 25 m/s. It

strikes the ground after 2.0 s. How high is the building, assuming negligible air resistance?

A) 20 m

B) 30 m

C) 50 m

D) 70 m

76) A ball is thrown straight up with a speed of 30 m/s, and air resistance is negligible.

(a) How long does it take the ball to reach the maximum height?

(b) What is the maximum height reached by the ball?

77) A foul ball is hit straight up into the air with a speed of 30 m/s, and air resistance is

negligible.

(a) Calculate the time required for the ball to rise to its maximum height.

(b) Calculate the maximum height reached by the ball above the point where it hit the bat.

the bat.

(d) Explain why there are two answers to part (c).

78) A ball is projected upward at time t = 0 s, from a point on a flat roof 10 m above the ground.

The ball rises and then falls with insignificant air resistance, missing the roof, and strikes the

ground. The initial velocity of the ball is Consider all quantities as positive in the

upward direction. At time the vertical velocity of the ball is closest to

A) 0 m/s.

B) +175 m/s.

C) +12 m/s.

D) -175 m/s.

E) -12 m/s.

79) A ball is projected upward at time t = 0 s, from a point on a flat roof 90 m above the ground.

The ball rises and then falls with insignificant air resistance, missing the roof, and strikes the

ground. The initial velocity of the ball is Consider all quantities as positive in the

upward direction. The vertical velocity of the ball when it is above the ground is closest to

A) -81 m/s.

B) -64 m/s.

C) -48 m/s.

D) -32 m/s.

E) -97 m/s.

80) A test rocket at ground level is fired straight up from rest with a net upward acceleration of

20 m/s2. After 4.0 s, the motor turns off but the rocket continues to coast upward with

insignificant air resistance. What maximum elevation does the rocket reach?

A) 160 m

B) 330 m

C) 320 m

D) 410 m

E) 490 m

81) A toy rocket is launched vertically from ground level at time t = 0.00 s. The rocket engine

provides constant upward acceleration during the burn phase. At the instant of engine burnout,

the rocket has risen to 64 m and acquired an upward velocity of The rocket continues to

rise with insignificant air resistance in unpowered flight, reaches maximum height, and falls back

to the ground. The time interval during which the rocket engine provided the upward

acceleration, is closest to

A) 2.1 s.

B) 2.3 s.

C) 1.9 s.

D) 1.7 s.

E) 1.5 s.

82) A toy rocket is launched vertically from ground level at time t = 0.00 s. The rocket engine

provides constant upward acceleration during the burn phase. At the instant of engine burnout,

the rocket has risen to 81 m and acquired an upward velocity of The rocket continues to

rise with insignificant air resistance in unpowered flight, reaches maximum height, and falls back

to the ground. The upward acceleration of the rocket during the burn phase is closest to

A) 9.9 m/ .

B) 9.6 m/ .

C) 9.3 m/ .

D) 9.0 m/ .

E) 8.7 m/ .