Deck 2: Motion in One Dimension

Question 1

You are traveling in your car at 82 km/h (23 m/s) when an emergency arises. If your car is 4 m long, how many car lengths do you travel during the 0.7 s of reaction time (i.e., the time interval between seeing the emergency and hitting the brake with your foot)?

A) 2
B) 4
C) 6
D) 8
E) 10

Answer 1

4

Question 2

The displacement of an object during any time interval is always ________ the distance it travels during that same time interval.

A) greater than or equal to
B) less than or equal to
C) equal to
D) greater than
E) much greater than

Answer 2

less than or equal to

Question 3

The displacement of an object for a round trip between two locations

A) is always greater than zero.
B) is always less than zero.
C) is zero.
D) can be greater than or less than but not equal to zero.
E) can have any value.

Answer 3

is zero.

Question 4

You drive for 30 min at 100 km/h and then stop for 15 min. You then drive for 45 min at 80 km/h. Your average speed for the entire trip is

A) 73 km/h.
B) 83 km/h.
C) 88 km/h.
D) 90 km/h.
E) 97 km/h.

Question 5

A river 1.00 mile wide flows with a constant speed of 1.00 mi/h. A man can row a boat at 2.00 mi/h. He crosses the river in a direction that puts him directly across the river from the starting point, and then he returns in a direction that puts him back at the starting point in the shortest time possible. The travel time for the man is

A) 2.00 h.
B) 1.15 h.
C) 1.00 h.
D) 1.33 h.
E) 0.67 h.

Question 6

Use the following to answer question :
In which graph of v versus t does the particle end up closest to its starting point?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 7

Four successive displacements of 4 km, 5 km, 4 km, and 2 km are at right angles to each other as shown in the diagram. The magnitude of the resultant displacement is

A) 4 km
B) 15 km
C) 3 km
D) 5 km
E) None of these is correct.

Question 8

The graph shows how the position of a particle depends on time. Which choice is closest to the average speed of the particle in the time interval between 0 and 6 s?

A) 0.40 m/s
B) 0.67 m/s
C) 0.75 m/s
D) 1.50 m/s
E) 2.22 m/s

Question 9

Assume that the Deschutes River has straight and parallel banks and that the current is 0.75 m/s. Drifting down the river, you fall out of your boat and immediately grab a piling of the Warm Springs Bridge. You hold on for 40 s and then swim after the boat with a speed relative to the water of 0.95 m/s. The distance of the boat downstream from the bridge when you catch it is

A) 67 m.
B) 90 m.
C) 78 m.
D) 54 m.
E) 120 m.

Question 10

Four successive displacements of 3 km, 4 km, 5 km, and 4 km are at right angles to each other as shown in the diagram. The magnitude of the resultant displacement is

A) 2 km
B) 16 km
C) 3 km
D) 5 km
E) None of these is correct.

Question 11

A particle moves from x₀ = 30 cm to x = -40 cm in 5 s. The average velocity of the particle during this time interval is

A) 2 cm/s.
B) -2 cm/s.
C) 14 cm/s.
D) -14 cm/s.
E) -140 cm/s.

Question 12

An object, located at the origin when t = 0, moves along the x axis as shown in the diagram. At which point is the object farthest from its starting point?

A) A
B) B
C) C
D) D
E) E

Question 13

You drive for 30 min for 30 km East and then another 30 min for 40 km North. Your average velocity for the entire trip is

A) 40 km/h.
B) 50 km/h.
C) 60 km/h.
D) 70 km/h.
E) 80 km/h.

Question 14

You drive for 30 min for 30 km East and then another 30 min for 40 km North. Your average speed for the entire trip is

A) 40 km/h.
B) 50 km/h.
C) 60 km/h.
D) 70 km/h.
E) 80 km/h.

Question 15

If the speed of particle A is twice that of particle B, the distance particle B travels in a given interval of time as compared with particle A is

A) twice as great.
B) half as great.
C) the same.
D) four times as great.
E) one-fourth as great.

Question 16

Use the following to answer question :
In which graph of v versus t does the particle end up farthest from its starting point?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 17

A particle moves from x₁ = -50 cm to x₂ = 30 cm. The displacement of this particle is

A) -50 cm
B) 30 cm
C) 80 cm
D) -30 cm
E) -80 cm

Question 18

A particle moves from x₁ = 30 cm to x₂ = - 40 cm. The displacement of this particle is

A) 30 cm
B) 40 cm
C) 70 cm
D) -70 cm
E) - 40 cm

Question 19

A river 1.00 mile wide flows with a constant speed of 1.00 mi/h. A woman leaves from a point on the river bank. The woman rows a boat 1.00 mi directly upstream and returns to the starting point. Her speed in still water is 2.00 mi/h. The travel time for the woman is

A) 2.00 h.
B) 1.15 h.
C) 1.00 h.
D) 1.33 h.
E) 0.67 h.

Question 20

Use the following to answer question :
Which graph of v versus t best describes the motion of a particle whose velocity is constant and negative?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 21

If the position of an object is plotted vertically on a graph and the time is plotted horizontally, the instantaneous velocity at a particular time is

A) the height of the curve at that time.
B) the total length of the curve.
C) the slope of the tangent to the curve at that time.
D) the area under the curve from zero to that time.
E) impossible to determine from this type of plot.

Question 22

The graph represents the displacement of a particle along the x axis as a function of time. The interval in which the velocity of this particle is negative is

A) a-b
B) b-c
C) d-e
D) c-d
E) none of these is correct.

Question 23

In which graph is the particle the farthest from the origin at t = 5 s?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 24

An airplane flies 600 miles with a tail wind in 2.0 hrs. If it takes 2.5 hrs to cover the same distance against the headwind, then what is the speed of the plane in still air?

A) 270 mph
B) 300 mph
C) 240 mph
D) 330 mph
E) 250 mph

Question 25

The distance traveled by a car in the x-direction is shown. When the car changes speed for t = 10 s to 15 s, it does so uniformly. Use the graph below to answer the next question.
The speed of the car at 17.5 s is

A) 5 m/s
B) 10 m/s
C) 15 m/s
D) 20 m/s
E) 25 m/s

Question 26

-For this problem, refer to the figure in problem 31. Which point has the highest instantaneous velocity?

A) a
B) b
C) c
D) d
E) e

Question 27

It takes the Mars rover 4.5 minutes to send information via a radio signal traveling at the speed of light back to Mission Control on Earth. How far away is the rover?

A) 8.1 $\times$ 10¹⁰ km
B) 1.35 $\times$ 10⁹ m
C) 8.10 $\times$ 10¹⁰ m
D) 1.35 $\times$ 10⁹ km
E) 1.62 $\times$ 10¹¹ m

Question 28

The distance traveled by a car in the x-direction is shown. When the car changes speed for t = 10 s to 15 s, it does so uniformly. Use the graph below to answer the next question.
The speed of the car at 5 s is

A) 5 m/s
B) 7.5 m/s
C) 10 m/s
D) 12.5 m/s
E) 15 m/s

Question 29

An object moves along the x axis as shown in the diagram. At which point or points is the object instantaneously at rest?

A) A and E
B) B, D, and E
C) C only
D) E only
E) None of these is correct.

Question 30

The distance traveled by a car in the x-direction is shown. When the car changes speed for t = 10 s to 15 s, it does so uniformly. Use the graph below to answer the next question.

-The speed of the car at 5 s is ____ speed at 20 s.

A) less than the
B) equal to the
C) greater than the
D) unable to tell
E) depends on what happens when it is accelerating between 10 and 15 s.

Question 31

-For this problem, refer to the figure in problem 31. Which interval has the highest magnitude in acceleration?

A) a-b
B) b-c
C) c-d
D) d-e
E) they have equal acceleration

Question 32

The graph shows how the position of a particle depends on time. Which choice is closest to the instantaneous speed of the particle at t = 3 s?

A) 0.40 m/s
B) 0.67 m/s
C) 0.75 m/s
D) 1.50 m/s
E) 2.22 m/s

Question 33

On a graph that shows position on the vertical axis and time on the horizontal axis, a straight line with a positive slope represents

A) a constant positive acceleration.
B) a constant negative acceleration.
C) zero velocity.
D) a constant positive velocity.
E) a constant negative velocity.

Question 34

The graph shows the velocity of a particle as a function of time. In the 12 s shown, the particle travels

A) 0 m.
B) 1200 m.
C) 640 m.
D) 440 m.
E) 200 m.

Question 35

The graph shows the displacement of a particle along the y axis as a function of time. The points at which the velocity is the same are

A) A and C.
B) A and E.
C) B and D.
D) A, C, and E.
E) B, C, and D.

Question 36

An object moves along the x axis as shown in the diagram. At which point or points is the magnitude of its velocity a minimum?

A) A and E
B) B, D, and E
C) C only
D) E only
E) None of these is correct.

Question 37

A Ford truck enters a highway and travels at a uniform speed of 50 mph. Half an hour later a Jaguar enters the highway at the same junction and heads in the same direction at 55 mph. How long after the Ford entered the highway does the Jaguar catch up with the truck?

A) 5.0 hrs
B) 6.0 hrs
C) 1.0 hrs
D) 1.6 hrs
E) 5.5 hrs

Question 38

In which graph is the particle the closest to the origin at t = 5 s?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 39

If an object is moving at uniform speed in a straight line, its instantaneous velocity halfway through any time interval is

A) greater than its average velocity.
B) less than its average velocity.
C) the same as its average velocity.
D) half of its average velocity.
E) twice its average velocity.

Question 40

On a graph that shows position on the vertical axis and time on the horizontal axis, a straight line with a negative slope represents

A) a constant positive acceleration.
B) a constant negative acceleration.
C) zero velocity.
D) a constant positive velocity.
E) a constant negative velocity.

Question 41

On a graph that shows velocity on the vertical axis and time on the horizontal axis, constant acceleration is represented by

A) a straight line with a positive slope.
B) a straight line with a negative slope.
C) a straight line with zero slope.
D) either a, b, or c.
E) None of these is correct.

Question 42

An object is moving in a straight line. At t = 0, its speed is 5.0 m/s. From t = 0 to t = 4.0 s, its acceleration is 2.5 m/s². From t = 4.0 s to t = 11.0 s, its speed is constant. The average speed over the entire time interval is

A) 9.5 m/s
B) 15 m/s
C) 13 m/s
D) 21 m/s
E) 8.2 m/s

Question 43

On a graph that shows position on the vertical axis and time on the horizontal axis, a parabolic curve that opens upward represents

A) a constant positive acceleration.
B) a constant negative acceleration.
C) no acceleration.
D) a positive followed by a negative acceleration.
E) a negative followed by a positive acceleration.

Question 44

A vehicle is traveling in the +x direction to x = 100 m. It then reverses direction. At the instant when it changes direction, the acceleration of the vehicle is

A) positive.
B) negative.
C) zero.
D) positive then negative.
E) negative then positive.

Question 45

On a graph that shows velocity on the vertical axis and time on the horizontal axis, zero acceleration is represented by

A) a straight line with a positive slope.
B) a straight line with a negative slope.
C) a straight line with zero slope.
D) either a, b, or c.
E) None of these is correct.

Question 46

The distance traveled by a car in the x-direction is shown. When the car changes speed for t = 10 s to 15 s, it does so uniformly. Use the graph below to answer the next question.
The acceleration of the car between 10 s and 15 s is

A) 1 m/s²
B) 2 m/s²
C) 3 m/s²
D) 4 m/s²
E) 5 m/s²

Question 47

On a graph that shows velocity on the vertical axis and time on the horizontal axis, the area under the curve represents

A) Average acceleration.
B) Average velocity.
C) displacement.
D) average speed.
E) no useful physical quantity.

Question 48

On a graph that shows position on the vertical axis and time on the horizontal axis, the area under the curve represents

A) average acceleration.
B) average velocity.
C) displacement.
D) average speed.
E) nothing of physical significance.

Question 49

Use the following to answer question :
In which graph of v versus t is the magnitude of the particle's acceleration the greatest?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 50

A Triumph sports car starts at rest and accelerates uniformly to a speed of 27.0 m/s in 11.8 s. Calculate the distance the car travels during this time interval.

A) 160 m
B) 320 m
C) 1.90 km
D) 640 m
E) 350 m

Question 51

For uniformly accelerated motion, which of the following quantities must be zero?

A) the initial velocity
B) the initial displacement
C) the rate of change of the acceleration
D) the rate of change of the velocity
E) the rate of change of the displacement

Question 52

A particle accelerates uniformly from a speed of 30 cm/s to 40 cm/s in 5 s and thereafter moves at a constant speed of 40 cm/s for an additional 3 s. The average speed over this total time interval is

A) 35 cm/s
B) 27 cm/s
C) 0.45 cm/s
D) 37 cm/s
E) 73 cm/s

Question 53

Use the following to answer question :
Which graph of v versus t best describes the motion of a particle with positive velocity and negative acceleration?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 54

The distance traveled by a car in the x-direction is shown. When the car changes speed for t = 10 s to 15 s, it does so uniformly. Use the graph below to answer the next question.
The acceleration of the car at 5 s is ____ acceleration at 20 s.

A) less than the
B) equal to the
C) greater than the
D) unable to tell
E) depends on what happens when it is accelerating between 10 and 15 s

Question 55

A car accelerates uniformly from rest to a speed of 20 m/s at the end of 1 min; it then accelerates uniformly to a speed of 40 m/s at the end of the next minute. During this 2-min period, the average speed of the car is

A) 7.5 m/s
B) 30 m/s
C) 15 m/s
D) 20 m/s
E) 40 m/s

Question 56

A particle decelerates uniformly from a speed of 30 cm/s to rest in a time interval of 5.0 s. It then has a uniform acceleration of 10 cm/s² for another 5.0 s. The particle moves in the same direction along a straight line. The average speed over the whole time interval is

A) 20 cm/s
B) 35 cm/s
C) 38 cm/s
D) 100 cm/s
E) 12 cm/s

Question 57

A particle that is moving along a straight line decelerates uniformly from 40 cm/s to 20 cm/s in 5.0 s and then has a constant acceleration of 20 cm/s² during the next 4.0 s. The average speed over the whole time interval is

A) 57 cm/s
B) 140 cm/s
C) 86 cm/s
D) 43 cm/s
E) 97 cm/s

Question 58

A vehicle is traveling in the -x direction to x = 100 m. It then reverses direction. At the instant when it changes direction, the acceleration of the vehicle is

A) positive.
B) negative.
C) zero.
D) positive then negative.
E) negative then positive.

Question 59

On a graph that shows position on the vertical axis and time on the horizontal axis, a parabolic curve that opens downward represents

A) a constant positive acceleration.
B) a constant negative acceleration.
C) no acceleration.
D) a positive followed by a negative acceleration.
E) a negative followed by a positive acceleration.

Question 60

Use the following to answer question :
Which graph of v versus t best describes the motion of a particle with negative velocity and negative acceleration?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 61

If we assume that a spaceship could accelerate from rest at a constant rate of 9.81 m/s², then how long would it take to reach 1% of the speed of light? (Assume the speed of light = 3.0 $\times$ 10⁸ m/s)

A) 1.8 days
B) 3.5 days
C) 3.1 $\times$ 10⁴ s
D) 3.1 $\times$ 10⁶ s
E) 7.1 days

Question 62

A car is traveling at 120 km/h (75 mph). When applied the braking system can stop the car with a deceleration rate of 9.0 m/s². The typical reaction time for an alert driver is 0.5 s versus 2 s for a sleepy driver. Assuming a typical car length of 5 m, calculate the number of additional car lengths it takes the sleepy driver to stop compared to the alert driver.

A) 13
B) 3.0
C) 10
D) 16
E) 26

Question 63

A car accelerates uniformly from a velocity of 10 km/h to 30 km/h in one minute. Which graph best describes the motion of the car?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 64

A common statistic in car tests is the standing (starting from rest) quarter-mile performance. A modern sports car can achieve a terminal speed (speed at the end of the quarter-mile) of 120 mph (193 km/h). How does the average acceleration compare to g? (0.25 mile = 402 m)

A) 0.36 g
B) 2.8 g
C) 0.067 g
D) 15.0 g
E) 0.73 g

Question 65

An object is at x = -3 m and has a velocity of 4 m/s. It is observed to be slowing down. Its acceleration is

A) positive.
B) negative.
C) zero.
D) negative until the object stops and then positive.
E) impossible to determine based on the information provided.

Question 66

Use the following to answer question :
In which graph does the particle have a constant acceleration for the entire 5 s?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 67

An object moves along the horizontal axis as shown on the diagram. At which point or points is its acceleration zero?

A) A and E
B) B, D, and E
C) C only
D) E only
E) B and D

Question 68

An object is dropped from rest near the surface of Earth. If the time interval during which it falls is doubled, the distance it falls will

A) double.
B) decrease by one-half.
C) increase by a factor of four.
D) decrease by a factor of four.
E) not change.

Question 69

A car and a truck, starting from rest, have the same acceleration, but the truck accelerates for twice the length of time. Compared with the car, the truck will travel

A) twice as far.
B) three times as far.
C) 1.4 times as far.
D) four times as far.
E) one-half as far.

Question 70

A racecar starts from rest and accelerates at a constant rate and reaches a speed of 160 km/h (100 mph) in 6.0 seconds. It continues at this speed for another 5 seconds. What is the car's average speed during the first 11 seconds?

A) 34.3 m/s
B) 29.3 m/s
C) 22.2 m/s
D) 32.3 m/s
E) 44.4 m/s

Question 71

A Lamborghini sports car can accelerate from zero to 60 mph in 4 seconds. It can decelerate from 60 mph to rest in 120 ft. What is the ratio of average acceleration over average deceleration? (1 mile = 5280 ft)

A) 1.74 $\times$ 10^-5
B) 1.47
C) 0.682
D) 0.0114
E) 0.688

Question 72

An object is at x = -3 m and has a velocity of - 4 m/s. It is observed to be slowing down. Its acceleration is

A) positive.
B) negative.
C) zero.
D) negative until the object stops and then positive.
E) impossible to determine based on the information provided.

Question 73

Use the following to answer question :
In which graph does the particle have no acceleration at t = 5 s?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 74

An object falling near the surface of Earth has a constant acceleration of 9.8 m/s². This means that the

A) object falls 9.8 m during the first second of its motion.
B) object falls 9.8 m during each second of its motion.
C) speed of the object increases by 9.8 m/s during each second of its motion.
D) acceleration of the object increases by 9.8 m/s² during each second of its motion.
E) force of gravity on the object must be 9.8 SI units.

Question 75

A projectile is fired vertically upward with a speed of 62 m/s. In the absence of air resistance, the maximum height the projectile attains is

A) 25 km
B) 98 m
C) 200 m
D) 19 km
E) 3 m

Question 76

An object is dropped from rest near the surface of Earth. If the time interval during which it falls is cut in half, the distance it falls will

A) double.
B) decrease by one-half.
C) increase by a factor of four.
D) decrease by a factor of four.
E) not change.

Question 77

A ball is dropped from the top of a building. In the absence of air resistance, the ball will hit the ground with a speed of 49 m/s. The height of the building is

A) 25 m
B) 5 m
C) 240 m
D) 120 m
E) 10 m

Question 78

If we assume that a spaceship could accelerate from rest up to 1% of the speed of light at a constant rate of 9.81 m/s², how many times the radius of our Solar System (i.e., the distance from the Sun to Pluto = 5.9 $\times$ 10⁹ km) would the spaceship have traveled?

A) 78
B) 7.8 $\times$ 10^-2
C) 2.6 $\times$ 10^-10
D) 2.6 $\times$ 10^-7
E) 7.8 $\times$ 10^-1

Question 79

Use the following to answer question :
In which graph does the particle never have a constant acceleration?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 80

A graph of the motion of an object is plotted with the velocity on the vertical axis and the time on the horizontal axis. The graph is a straight line. Which of these quantities CANNOT be determined from this graph?

A) the displacement from time t = 0
B) the initial velocity at t = 0
C) the acceleration of the object
D) the average velocity of the object
E) All four of the quantities can be determined from the graph.