Deck 2: Motion Along a Straight Line

Question 1

This graph shows the position of a particle as a function of time. What is its average velocity between t = 5s and t = 9s?

A) 3 m/s
B) -3 m/s
C) 12 m/s
D) -12 m/s
E) Need additional information.

Answer 1

-3 m/s

Question 2

Two automobiles are 150 kilometers apart and traveling toward each other. One automobile is moving at 60 km/h and the other is moving at 40 km/h. In how many hours will they meet?

A) 2.5 h
B) 2.0 h
C) 1.75 h
D) 1.5 h
E) 1.25 h

Answer 2

1.5 h

Question 3

Each of four particles moves along an x axis. Their coordinates (in meters) as functions of time (in seconds) are given by For which of these particles is the velocity increasing for t > 0?

A) All four
B) Only 1
C) Only 2 and 3
D) Only 2, 3, and 4
E) None of them

Answer 3

Only 2 and 3

Question 4

Which of the following five coordinate versus time graphs represents the motion of an object whose speed is increasing?

A) I
B) II
C) III
D) IV
E) V

Question 5

The average speed of a moving object during a given interval of time is always:

A) the magnitude of its average velocity over the interval
B) the distance covered during the time interval divided by the time interval
C) one-half its speed at the end of the interval
D) its acceleration multiplied by the time interval
E) one-half its acceleration multiplied by the time interval.

Question 6

The coordinate-time graph of an object is a straight line with a positive slope. The object has:

A) constant displacement
B) steadily increasing acceleration
C) steadily decreasing acceleration
D) constant velocity
E) steadily increasing velocity

Question 7

A car travels 40 kilometers at an average speed of 80 km/h and then travels 40 kilometers at an average speed of 40 km/h. The average speed of the car for this 80 km trip is:

A) 40 km/h
B) 45 km/h
C) 53 km/h
D) 60 km/h
E) 80 km/h

Question 8

A particle moves along the x axis from x_i to x _f . Of the following values of the initial and final coordinates, which results in a negative displacement?

A) x_i = 4m, x _f = 6m
B) x_i = -4m, x _f = -8m
C) x_i = -4m, x _f = 2m
D) x_i = -4m, x _f = -2m
E) x_i = -4m, x _f = 4m

Question 9

When can you treat a moving object as if it were a point-like particle?

A) Only if it really is a point-like particle.
B) You can always treat a moving object as if it were a point-like particle.
C) Only if the object is moving with constant acceleration.
D) Only if all parts of the object are moving in the same direction and at the same rate.
E) This question has no physical meaning.

Question 10

A particle moves along the x axis from x_i to x _f . Of the following values of the initial and final coordinates, which results in the displacement with the largest magnitude?

A) x_i = 4m, x _f = 6m
B) x_i = -4m, x _f = -8m
C) x_i = -4m, x _f = 2m
D) x_i = 4m, x _f = -2m
E) x_i = -4m, x _f = 4m

Question 11

This graph shows the position of a particle as a function of time. What is its instantaneous velocity at t = 7s?

A) 3 m/s
B) -3 m/s
C) 12 m/s
D) -12 m/s
E) Need additional information.

Question 12

The coordinate of a particle in meters is given by x(t) = 16t - 3.0t³, where the time t is in seconds. The particle is momentarily at rest at t =

A) 0.75 s
B) 1.3 s
C) 1.8 s
D) 5.3 s
E) 7.3 s

Question 13

The coordinate of an object is given as a function of time by x = 7t - 3t², where x is in meters and t is in seconds. Its velocity at t = 3s is:

A) -6 m/s
B) -11 m/s
C) -21 m/s
D) 9 m/s
E) 18 m/s

Question 14

Which of the following five coordinate versus time graphs represents the motion of an object moving with a constant nonzero speed?

A) I
B) II
C) III
D) IV
E) V

Question 15

A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around, and returns to Hither. The time for this round trip is 2 hours. The average speed of the car for this round trip is:

A) 0 km/h
B) 25 km/h
C) 50 km/h
D) 100 km/h
E) cannot be calculated without knowing the acceleration

Question 16

The position y of a particle moving along the y axis depends on the time t according to the equation y = at - bt². The dimensions of the quantities a and b are respectively:

A) L²/T, L³/T²
B) L/T², L²/T
C) L/T, L/T²
D) L³/T, T²/L
E) none of these

Question 17

A particle moves from point x₁ to point x₂. Its displacement is given by:

A) x₂ - x₁
B) x₁ - x₂
C) x₁ + x₂
D) x₁
E) x₂

Question 18

A car starts from Hither, goes 50 km in a straight line to Yon, immediately turns around, and returns to Hither. The time for this round trip is 2 hours. The magnitude of the average velocity of the car for this round trip is:

A) 0 km/hr
B) 50 km/hr
C) 100 km/hr
D) 200 km/hr
E) cannot be calculated without knowing the acceleration

Question 19

You leave your house and drive to your friend's house, where you stay a while. Then you come back home. Which of the following must be true of your trip?

A) Your instantaneous velocity was never zero.
B) Your average velocity was zero.
C) Your acceleration was constant.
D) Your net displacement was not zero.
E) Your average speed was zero.

Question 20

The coordinate of an object is given as a function of time by x = 7t - 3t², where x is in meters and t is in seconds. Its average velocity over the interval from t = 0 to t = 2 s is:

A) 5 m/s
B) -5 m/s
C) 11 m/s
D) -11 m/s
E) 1 m/s

Question 21

The diagram shows a velocity-time graph for a car moving in a straight line. At point P the car must be:

A) moving with zero acceleration
B) climbing the hill
C) accelerating
D) stationary
E) moving at about 45° with respect to the x axis

Question 22

Starting at time t = 0, an object moves along a straight line. Its coordinate in meters is given by x(t) = 75t - 1.0t³, where t is in seconds. When it momentarily stops its acceleration is:

A) 0 m/s²
B) -73 m/s²
C) -30 m/s²
D) -9.8 m/s²
E) 9.2 x 10³ m/s²

Question 23

Over a short interval, starting at time t = 0, the coordinate of an automobile in meters is given by x(t) = 27t - 4.0t³, where t is in seconds. The magnitudes of the initial (at t = 0) velocity and acceleration of the auto respectively are:

A) 0 m/s; 12 m/s²
B) 0 m/s; 24 m/s²
C) 27 m/s; 0 m/s²
D) 27 m/s; 12 m/s²
E) 27 m/s; 24 m/s²

Question 24

The diagram represents the straight line motion of a car. Which of the following statements is true?

A) The car's speed increases, then it stops, and reverses
B) The car accelerates at 6 m/s² for the first 2 s
C) The car is moving for a total time of 12 s
D) The car accelerates at -12 m/s² for the last 4 s
E) The car returns to its starting point when t = 9 s

Question 25

Which of the following five acceleration versus time graphs is correct for an object moving in a straight line at a constant velocity of 20 m/s?

A) I
B) II
C) III
D) IV
E) V

Question 26

Over a short interval near time t = 0 the coordinate of an automobile in meters is given by x(t) = 27t - 4.0t³, where t is in seconds. At the end of 1.0 s the acceleration of the auto is:

A) 23 m/s²
B) 15 m/s²
C) -4.0 m/s²
D) -12 m/s²
E) -24 m/s²

Question 27

Is it possible for an object to have zero velocity and constant nonzero acceleration?

A) Yes, but only if it is not moving at all.
B) No, if its velocity is zero its acceleration must also be zero.
C) Yes, all objects with zero velocity have nonzero acceleration.
D) No, if its acceleration is not zero its velocity cannot be zero.
E) Yes, but its velocity must only be zero for an instant.

Question 28

Can an object have positive acceleration and decreasing speed?

A) No, this is not possible.
B) Yes, speed will always decrease if acceleration is positive.
C) Yes, this is possible if the initial velocity is zero.
D) Yes, this is possible if the initial velocity is negative.
E) Yes, this is possible but only if the object is moving in two dimensions.

Question 29

All falling objects experience some air resistance, the effect of which is to decrease acceleration. When the falling object's acceleration reaches zero, the acceleration stops changing. Therefore, if you drop an object and it falls far enough for this to happen,

A) its speed continues to increase all the way down.
B) its speed reaches a maximum value and then decreases.
C) its speed reaches a maximum value and then doesn't change.
D) its speed reaches a maximum value, decreases, and then increases again.
E) Any of these things could happen.

Question 30

A particle moves on the x axis. When its acceleration is positive and increasing:

A) its velocity must be positive
B) its velocity must be negative
C) it must be slowing down
D) it must be speeding up
E) none of the above must be true

Question 31

The coordinate of an object is given as a function of time by x = 4t² - 3t³, where x is in meters and t is in seconds. Its average acceleration over the interval from t = 0 to t = 2 s is:

A) -8 m/s²
B) 4 m/s²
C) -10 m/s²
D) 10 m/s²
E) -13 m/s²

Question 32

Each of four particles moves along an x axis. Their coordinates (in meters) as functions of time (in seconds) are given by Which of these particles have constant acceleration?

A) All four
B) Only 1 and 2
C) Only 2 and 3
D) Only 3 and 4
E) None of them

Question 33

The diagram shows a velocity-time graph for a car moving in a straight line. At point Q the car must be:

A) moving with zero acceleration
B) traveling downhill
C) traveling below ground-level
D) reducing speed
E) traveling in the reverse direction to that at point P

Question 34

What is the relationship between instantaneous speed and instantaneous velocity?

A) They are identical.
B) Instantaneous speed is the rate at which the instantaneous velocity is changing.
C) Instantaneous speed is the magnitude of the instantaneous velocity.
D) They are unrelated.
E) Instantaneous speed is the initial speed minus the final speed.

Question 35

A particle moves along the x axis according to the equation x = 6t² where x is in meters and t is in seconds. Therefore:

A) the acceleration of the particle is 6 m/s²
B) t cannot be negative
C) the particle follows a parabolic path
D) each second the velocity of the particle changes by 9.8 m/s
E) none of the above

Question 36

Throughout a time interval, while the speed of a particle increases as it moves along the x axis, its velocity and acceleration could be:

A) positive and negative, respectively
B) negative and positive, respectively
C) negative and negative, respectively
D) negative and zero, respectively
E) positive and zero, respectively

Question 37

A ball rolls up a slope. At the end of three seconds its velocity is 20 cm/s; at the end of eight seconds its velocity is 0 cm/s. What is the magnitude of its average acceleration from the third to the eighth second?

A) 2.5 cm/s²
B) 4.0 cm/s²
C) 5.0 cm/s²
D) 6.0 cm/s²
E) 6.67 cm/s²

Question 38

Of the following situations, which one is impossible?

A) A body having velocity east and acceleration east
B) A body having velocity east and acceleration west
C) A body having zero velocity and non-zero acceleration
D) A body having constant acceleration and variable velocity
E) A body having constant velocity and variable acceleration

Question 39

Starting at time t = 0, an object moves along a straight line with velocity in m/s given by v(t) = 98 - 2t², where t is in seconds. When it momentarily stops its acceleration is:

A) 0 m/s²
B) -4.0 m/s²
C) -9.8 m/s²
D) -28 m/s²
E) 49 m/s²

Question 40

A car accelerates from rest on a straight road. A short time later, the car decelerates to a stop and then returns to its original position in a similar manner, by speeding up and then slowing to a stop. Which of the following five coordinate versus time graphs best describes the motion?

A) I
B) II
C) III
D) IV
E) V

Question 41

At time t = 0 a car has a velocity of 16 m/s. It slows down with an acceleration given by a = -0.50t, in m/s² for t in seconds. It stops at t =

A) 64 s
B) 32 s
C) 16 s
D) 8.0 s
E) 4.0 s

Question 42

A drag racing car starts from rest at t = 0 and moves along a straight line with velocity given by v = bt², where b is a constant. The expression for the distance traveled by this car from its position at t = 0 is:

A) bt³
B) bt³/3
C) 4bt²
D) 3bt²
E) bt^3/2

Question 43

A car moving with an initial velocity of 25 m/s north has a constant acceleration of 3 m/s² south. After 6 seconds its velocity will be:

A) 7 m/s north
B) 7 m/s south
C) 43 m/s north
D) 20 m/s north
E) 20 m/s south

Question 44

The area under a velocity-time graph represents:

A) acceleration
B) change in acceleration
C) speed
D) change in velocity
E) displacement

Question 45

The graph represents the straight line motion of a car. How far does the car travel between t = 2 seconds and t = 5 seconds?

A) 4 m
B) 12 m
C) 24 m
D) 36 m
E) 60 m

Question 46

The acceleration of an object, starting from rest, is shown in the graph below. Other than at t = 0, when is the velocity of the object equal to zero?

A) During the interval from 1.0 s to 3.0 s
B) At t = 3.5 s
C) At t = 4.0 s
D) At t = 5.0 s
E) At no other time less than or equal to 5 s.

Question 47

The velocity of an object is given as a function of time by v = 4t - 3t², where v is in m/s and t is in seconds. Its average velocity over the interval from t = 0 s to t = 2 s:

A) is 0
B) is -2 m/s
C) is 2 m/s
D) is -4 m/s
E) cannot be calculated unless the initial position is given

Question 48

Displacement can be obtained from:

A) the slope of an acceleration-time graph
B) the slope of a velocity-time graph
C) the area under an acceleration-time graph
D) the area under a velocity-time graph

Question 49

A car, initially at rest, travels 20 m in 4 s along a straight line with constant acceleration. The acceleration of the car is:

A) 1.3 m/s²
B) 2.5 m/s²
C) 4.9 m/s²
D) 9.8 m/s²
E) There is not enough information to answer this question.

Question 50

A car starts from rest and goes down a slope with a constant acceleration of 5 m/s². After 5 seconds the car reaches the bottom of the hill. What is its speed at the bottom of the hill?

A) 1 m/s
B) 12.5 m/s
C) 25 m/s
D) 50 m/s
E) 160 m/s

Question 51

At time t = 0 a car has a velocity of 16 m/s. It slows down with an acceleration given by a = -0.50t, in m/s² for t in seconds. At the end of 4.0 s it has traveled:

A) 0
B) 12 m
C) 14 m
D) 25 m
E) 59 m

Question 52

An object starts from rest and has a constant acceleration of 3 m/s². The position versus time graph for this object has a slope:

A) that increases with time
B) that is constant
C) that decreases with time
D) of 3 m/s
E) of 3 m/s²

Question 53

At time t = 0 a car has a velocity of 16 m/s. It slows down with an acceleration given by a = -0.50t, in m/s² for t in seconds. By the time it stops it has traveled:

A) 15 m
B) 31 m
C) 62 m
D) 85 m
E) 100 m

Question 54

An object with an initial velocity of 12 m/s west experiences a constant acceleration of 4 m/s² west for 3 seconds. During this time the object travels a distance of:

A) 18 m
B) 24 m
C) 36 m
D) 54 m
E) 144 m

Question 55

How far does a car travel in 6 s if its initial velocity is 2 m/s and its acceleration is 2 m/s² in the same direction as its initial velocity?

A) 12 m
B) 14 m
C) 24 m
D) 36 m
E) 48 m

Question 56

A racing car traveling with constant acceleration increases its speed from 10 m/s to 30 m/s over a distance of 60 m? How long does this take?

A) 2.0 s
B) 3.0 s
C) 5.0 s
D) 6.0 s
E) The time cannot be calculated since the speed is not constant

Question 57

At a stop light, a truck traveling at 15 m/s passes a car as it starts from rest. The truck travels at constant velocity and the car accelerates at 3 m/s². How much time does the car take to catch up to the truck?

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

Question 58

Consider the following five graphs (note the axes carefully). Which of these represent(s) motion at constant speed?

A) IV only
B) IV and V only
C) I, II, and III only
D) I and II only
E) I and IV only

Question 59

A ball is in free fall motion. Upward is taken to be the positive direction. The displacement of the ball is:

A) positive during both ascent and descent
B) negative during both ascent and descent
C) negative during ascent and positive during descent
D) positive during ascent and negative during descent
E) none of the above

Question 60

An object starts from rest at the origin and moves along the x axis with a constant acceleration of 4 m/s². Its average velocity as it goes from x = 2 m to x = 8 m is:

A) 1 m/s
B) 2 m/s
C) 3 m/s
D) 5 m/s
E) 6 m/s

Question 61

A freely falling body has a constant acceleration of 9.8 m/s². This means that:

A) the body falls 9.8 m during each second
B) the body falls 9.8 m during the first second
C) the speed of the body increases by 9.8 m/s during each second
D) the acceleration of the body increases by 9.8 m/s² during each second
E) the acceleration of the body decreases by 9.8 m/s² during each second

Question 62

A ball is thrown upwards. Its acceleration is:

A) downward during both ascent and descent
B) downward during ascent and upward during descent
C) upward during ascent and downward during descent
D) upward during both ascent and descent
E) downward at all times except at the very top, when it is zero

Question 63

An object is released from rest. How far does it fall during the second second of its fall?

A) 4.9 m
B) 9.8 m
C) 15 m
D) 20 m
E) 25 m

Question 64

An object is thrown vertically upward at 35 m/s. Taking g = 10 m/s², the velocity of the object 5 seconds later is:

A) 7.0 m/s up
B) 15 m/s down
C) 15 m/s up
D) 85 m/s down
E) 85 m/s up

Question 65

Neglecting the effect of air resistance, a stone dropped off a 175-m high building lands on the ground in:

A) 3 s
B) 4 s
C) 6 s
D) 18 s
E) 36 s

Question 66

An object is thrown straight up from ground level with a speed of 50 m/s. If g = 10 m/s² its distance above ground level 6.0 s later is:

A) 0.00 m
B) 270 m
C) 330 m
D) 480 m
E) none of these

Question 67

An object is shot vertically upward. While it is rising:

A) its velocity and acceleration are both upward
B) its velocity is upward and its acceleration is downward
C) its velocity and acceleration are both downward
D) its velocity is downward and its acceleration is upward
E) its velocity and acceleration are both decreasing

Question 68

A stone is thrown vertically upward with an initial speed of 19.5 m/s. It will rise to a maximum height of:

A) 4.9 m
B) 9.8 m
C) 19.4 m
D) 38.8 m
E) none of these

Question 69

A feather, initially at rest, is released in a vacuum 12 m above the surface of the Earth. Which of the following statements is correct?

A) The maximum velocity of the feather is 9.8 m/s
B) The acceleration of the feather decreases until terminal velocity is reached
C) The acceleration of the feather remains constant during the fall
D) The acceleration of the feather increases during the fall
E) The acceleration of the feather is zero

Question 70

Which of the following is NOT true of an object in free fall in the absence of air resistance?

A) Its acceleration is constant.
B) If its initial velocity is upwards, it will reach a maximum height and then begin to fall.
C) If its initial velocity is zero, its position below its starting point can be calculated knowing only how long ago it began falling.
D) Its velocity will always be zero at some point along its path.
E) Its velocity changes by the same amount every second.

Question 71

Which one of the following statements is correct for an object in free fall released from rest?

A) The average velocity during the first second of time is 4.9 m/s
B) During each second the object falls 9.8 m
C) The acceleration changes by 9.8 m/s every second
D) The object falls 9.8 m during the first second of time
E) The acceleration of the object is proportional to its weight

Question 72

An object is thrown straight up from ground level with a speed of 50 m/s. If g = 10 m/s² its distance above ground level 1.0 second later is:

A) 40 m
B) 45 m
C) 50 m
D) 55 m
E) 60 m

Question 73

A heavy ball falls freely, starting from rest. Between the third and fourth second of its fall it travels a distance of:

A) 4.9 m.
B) 9.8 m.
C) 29.4 m
D) 34.3 m.
E) 39.8 m.

Question 74

If you drop a rock and a feather, the rock hits the ground first. This demonstrates that:

A) The acceleration of gravity is not constant.
B) Heavier objects are accelerated faster by gravity than lighter objects are.
C) Air resistance has a larger effect on feathers than on rocks.
D) Rocks can't fly.
E) Gravity has little effect on a feather.

Question 75

A baseball is thrown vertically into the air. The acceleration of the ball at its highest point is:

A) zero
B) g, down
C) g, up
D) 2g. down
E) 2g, up

Question 76

At a location where g = 9.80 m/s², an object is thrown vertically down with an initial speed of 1.00 m/s. After 5.00 s the object will have traveled:

A) 125 m
B) 128 m
C) 245 m
D) 250 m
E) 255 m

Question 77

As a rocket is accelerating vertically upward at 9.8 m/s² near the Earth's surface, it releases a projectile. Immediately after release the acceleration of the projectile is:

A) 9.8 m/s² down
B) 0 m/s²
C) 9.8 m/s² up
D) 19.6 m/s² up
E) none of the above

Question 78

A stone is released from a balloon that is descending at a constant speed of 10 m/s. Neglecting air resistance, after 20 s the speed of the stone is:

A) 2160 m/s
B) 1760 m/s
C) 206 m/s
D) 196 m/s
E) 186 m/s

Question 79

An elevator is moving upward with constant acceleration. The dashed curve shows the position y of the ceiling of the elevator as a function of the time t. At the instant indicated by the dot, a bolt breaks loose and drops from the ceiling. Which curve best represents the position of the bolt as a function of time?

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

Question 80

An object dropped from a window of a tall building hits the ground in 12.0 s. If its acceleration is 9.80 m/s², the height of the window above the ground is (you may neglect air resistance):

A) 29.4 m
B) 58.8 m
C) 118 m
D) 353 m
E) 706 m