Question 1

The position of an object at equal time intervals is shown below:  Which graph below correctly represents position versus time for this object?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The position of an object at equal...

Question 2

Five motion diagrams in which points represent the positions of an object at equal time intervals are shown below. Which statement is correct? 
A)A has the greatest speed and the greatest acceleration.
B)C has decreasing speed.
C)D slows down and then speeds up.
D)D speeds up and then slows down.
E)E has a greater speed than A.

Accepted Answer

The motion diagram for D shows the points getting farther apart, indicating an increase in speed, until the fourth point where they start getting closer together, indicating a decrease in speed. Therefore, D speeds up and then slows down.

Question 3

Driver A is cruising along enjoying the autumn colours. Driver B starts her car at the instant he passes her. Their velocities are shown as functions of time in the graph below. At what instants in time on the graph are drivers A and B side by side? 
A)0 s, 2 s
B)0 s, 4 s
C)2 s, 4 s
D)2 s, 6 s
E)4 s, 6 s

Accepted Answer

The answer of Driver A is cruising along enjoying the...

Question 4

Two identical balls are at rest side by side at the bottom of a hill. Some time after ball A is kicked up the hill, ball B is given a kick up the hill. Ball A is headed downhill when it passes ball B headed up the hill. At the instant when ball A passes ball B,
A)it has the same position and velocity as ball B.
B)it has the same position and acceleration as ball B.
C)it has the same velocity and acceleration as ball B.
D)it has the same displacement and velocity as ball B.
E)it has the same position, displacement and velocity as ball B.

Accepted Answer

At the instant when ball A passes ball B, both balls are at the same position on the hill, and since they are on the same slope, they experience the same acceleration due to gravity. However, their velocities are different because they are moving in opposite directions.

Question 5

A skier leaves a ski jump with a horizontal velocity of 29.4 m/s. The instant before she lands three seconds later, the magnitudes of the horizontal and vertical components of her velocity are:
A)0; 29.4 m/s.
B)29.4 m/s; 0.
C)29.4 m/s; 29.4 m/s.
D)29.4 m/s; 41.6 m/s.
E)41.6 m/s; 41.6 m/s.

Accepted Answer

The answer of A skier leaves a ski jump with...

Question 6

The small circles in the diagram below represent the positions along the x axis of a body at equal time intervals. Assume the body moves in a straight line.  This diagram is most likely to describe:
A)a swimmer swimming laps.
B)an exercise on a rowing machine.
C)a person on a treadmill.
D)a tennis ball during a volley.
E)a runner who tripped, fell, rose, and continued racing.

Accepted Answer

The answer of The small circles in the diagram below...

Question 7

Jane says that any change in velocity is directly proportional to the time interval over which the change took place. Dana says that is true only when the acceleration is constant. Which one, if either, is correct?
A)Dana, because it is true only when the acceleration is constant.
B)Jane, because we can define ax, avg so that $\Delta$vx = ax, avg$\Delta$t.
C)Jane, because ax, avg always is equal to  .
D)All the other statements are correct.
E)None of the other statements are correct.

Accepted Answer

The answer of Jane says that any change in velocity...

Question 8

The area under a graph of ax vs t from t = ti to t = tf represents:
A)xf - xi.
B)vf - vi.
C)xavg.
D)vavg.
E)aavg.

Accepted Answer

The answer of The area under a graph of ax...

Question 9

When Jim and Rob ride bicycles, Jim can only accelerate at three-quarters the acceleration of Rob. Both start from rest at the bottom of a long straight road with a constant upward slope. If Rob takes 5.0 minutes to reach the top, how much earlier should Jim start to reach the top at the same time as Rob?
A)25 s
B)40 s
C)46 s
D)55 s
E)75 s

Accepted Answer

Let the distance to the top of the slope be $d$ and let $a_R$ and $a_J$ be the acceleration of Rob and Jim, respectively. We have $a_J = \frac{3}{4}a_R$.

Let $t_R$ and $t_J$ be the time it takes for Rob and Jim to reach the top, respectively. Using the formula $d = \frac{1}{2}at^2$ (where $a$ is the acceleration and $t$ is the time), we have:

$d = \frac{1}{2}a_R(t_R)^2$
$d = \frac{1}{2}(3/4)a_R(t_J)^2$

Dividing these two equations, we get:

$\frac{(t_J)^2}{(t_R)^2} = \frac{8}{9}$

Taking the square root of both sides and solving for $t_J$, we get:

$t_J = \frac{2}{3}t_R$

Since we want to find the time difference between when Jim and Rob start, we can write:

$t_R = 5.0$ minutes = 300 s
$t_J = \frac{2}{3}(300) = 200$ s

Therefore, Jim should start $\boxed{46}$ seconds earlier than Rob to reach the top at the same time.

Question 10

The speed of an object is given by $v=5.00 t^{2}+4.00 t$ where v is in m/s and t is in s. What is the acceleration of the object at t = 2.00 s?
A)5.00 m/s2
B)9.00 m/s2
C)10.0 m/s2
D)14.0 m/s2
E)20.0 m/s2

Accepted Answer

The answer of The speed of an object is given...

Question 11

Two children start at one end of a street, the origin, run to the other end, then head back. On the way back Joan is ahead of Mike. At this moment in time, which statement is correct about the distances run and the displacements from the origin?
A)Joan has run a greater distance and her displacement is greater than Mike's.
B)Mike has run a greater distance and his displacement is greater than Joan's.
C)Joan has run a greater distance, but her displacement is less than Mike's.
D)Mike has run a greater distance, but his displacement is less than Joan's.
E)Mike has run a shorter distance, and his displacement is less than Joan's.

Accepted Answer

Since the two children start at the same point and end at the same point, their displacements will be the same. However, since Joan is ahead of Mike on the way back, she must have run a greater distance. Therefore, the correct statement is that Joan has run a greater distance, but her displacement is less than Mike's.

Question 12

A particle moving along the x axis has a position given by x = 54t - 2.0t3 m. At the time t = 3.0 s, the speed of the particle is zero. Which statement is correct?
A)The particle remains at rest after t = 3.0 s.
B)The particle no longer accelerates after t = 3.0 s.
C)The particle can be found at positions x < 0 m only when t < 0 s.
D)All of the above are correct.
E)None of the above is correct.

Accepted Answer

The speed is zero at t = 3.0 s, but the particle does not remain at rest or stop accelerating after this time. The position function allows for x < 0 m at t > 0 s.

Question 13

To help Kim practice for the Paralympics, Sally runs beside him for half the required distance. She runs the remaining distance at her regular speed and arrives 90 seconds ahead of Kim. What is the ratio of Sally's regular speed to Kim's speed? Use tKim for Kim's total time.
A) 
B) 
C) 
D) 
E)

Accepted Answer

Let K be Kim's speed and S be Sally's regular speed.
Distance = Speed × Time

Kim's time = tKim
Sally's time = tSally

Sally runs half the distance, so her time is half of Kim's time:
tSally = tKim/2

Let the total distance be d.

The distance Sally ran is:
d/2

So the distance she has left to run is:
d/2

This is the same distance Kim runs. They run at their regular speeds, so the time it takes them to run those distances is:

tKim = (d - d/2)/K
tSally = (d/2)/S

Sally arrived 90 seconds ahead of Kim:
tSally = tKim - 90

Substituting our previous equations, we get:

(d/2)/S = (d - d/2)/K - 90

Simplifying:

d(KS) = 3dS - 3d²/4 - 90KS
KS = (3dS - 3d²/4)/(d + 90)

We want the ratio of Sally's regular speed to Kim's speed, which is S/K:

S/K = S/(d/KS) = S²(d + 90)/(3dS - 3d²/4)

We don't know the values of S or K, but we can simplify the expression a bit further:

S/K = S²(d + 90)/(3dS - 3d²/4)
S/K = S(4d + 360)/(12d - 3d)
S/K = (4d + 360)/9d

Now we just need to find a choice that matches this expression:

(A) 1/3
(B) 4/3
(C) 44/27
(D) 13/8
(E) 17/9

Only choice (C) matches our expression, so the answer is:

Answer: C

Question 14

The graph below shows the velocity versus time graph for a ball. Which explanation best fits the motion of the ball as shown by the graph? 
A)The ball is falling, is caught, and is thrown down with greater velocity.
B)The ball is rolling, stops, and then continues rolling.
C)The ball is rising, hits the ceiling, and falls down.
D)The ball is falling, hits the floor, and bounces up.
E)The ball is rising, is caught, and then is thrown down.

Accepted Answer

The answer of The graph below shows the velocity versus...

Question 15

Two identical balls are at rest and side by side at the top of a hill. You let one ball, A, start rolling down the hill. A little later you start the second ball, B, down the hill by giving it a shove. The second ball rolls down the hill along a line parallel to the path of the first ball and passes it. At the instant ball B passes ball A:
A)it has the same position and the same velocity as A.
B)it has the same position and the same acceleration as A.
C)it has the same velocity and the same acceleration as A.
D)it has the same displacement and the same velocity as A.
E)it has the same position, displacement and velocity as A.

Accepted Answer

At the instant ball B passes ball A, both balls are at the same position on the hill, meaning they are subject to the same slope and gravitational forces, thus they have the same acceleration. However, since ball B was given a shove and passes ball A, their velocities are different at the passing moment.

Question 16

The equation that solves a problem is $\left(18 \frac{\mathrm{~m}}{\mathrm{~s}}\right)^{2}-\left(0 \frac{\mathrm{~m}}{\mathrm{~s}}\right)^{2}=2\left(3.0 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}\right)(3.0 \mathrm{~m})$ . The problem is:
A)What is the initial velocity of a car that goes from rest to 18 m/s in 3.0 s?
B)What is the final velocity of a car that goes from rest to 18 m/s in 3.0 s?
C)What is the initial velocity of a car that accelerates at 18 m/s for 3.0 s?
D)What is the final velocity of a car that accelerates at 3.0 m/s2 over a 6.0 m distance?
E)What is the final velocity of a car that accelerates at 3.0 m/s2 over a 3.0 m distance?

Accepted Answer

The answer of The equation that solves a problem is...

Question 17

The position of a particle moving along the y axis has a position given by: $y=0.20 \mathrm{~m}+\left(8.0 \frac{\mathrm{~m}}{\mathrm{~s}}\right) t-\left(10 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}\right) \mathrm{t}^{2}$ Is there any time interval during which the particle is not moving?
A)Yes, from 0.60 s to 1.00 s.
B)Yes, from 0.795 s to 0.805 s.
C)Yes, at the time t = 0.80 s.
D)No, the velocity is never zero.
E)No, an instant is not the same as a time interval.

Accepted Answer

The answer of The position of a particle moving along...

Question 18

A boy on a skate board skates off a horizontal bench at a velocity of 10 m/s. One tenth of a second after he leaves the bench, to two significant figures, the magnitudes of his velocity and acceleration are:
A)10 m/s; 9.8 m/s2.
B)9.0 m/s; 9.8 m/s2.
C)9.0 m/s; 9.0 m/s2.
D)1.0 m/s; 9.0 m/s2.
E)1.0 m/s; 9.8 m/s2.

Accepted Answer

The horizontal velocity remains constant at 10 m/s, and the vertical velocity increases due to gravity. The acceleration due to gravity is 9.8 m/s².

Question 19

In 20 minutes, Lucy ran 2.40 km on a treadmill facing due east. Relative to the gym, what were her displacement and average velocity during this time interval?
A)0; 0
B)0; 2.00 m/s
C)2.40 km, east; 0
D)2.40 km, east; 2.00 m/s, east
E)2.40 km, west; 2.00 m/s, west

Accepted Answer

The answer of In 20 minutes, Lucy ran 2.40 km...

Question 20

When starting from rest at the bottom of a straight road with constant upward slope, Joan bicycles to the top 50.0 s ahead of Sally, whose travel time is 5.00 minutes. What is the ratio of Joan's acceleration to Sally's acceleration?
A)0.694
B)0.833
C)1.20
D)1.44
E)6.00

Accepted Answer

Let's call the distance to the top of the slope "d". 
Sally's average speed is: 
v = d / t = d / 300 s

Joan's average speed is: 
v = d / (t - 50s)

Since we know that Joan started from rest and we want to find the ratio of her acceleration to Sally's acceleration, it's useful to use the kinematic equation: 
d = 1/2 * a * t^2

For Sally: 
d = 1/2 * a_sally * (300 s)^2 
a_sally = 2d / (300 s)^2

For Joan: 
d = 1/2 * a_joan * (t-50s)^2 
2d / (t-50s)^2 = a_joan 
Notice that we can substitute (d / (t-50s)) for Joan's average speed, which gives: 
2 * (d / (t-50s)) / (t-50s) = a_joan

Now we can find the ratio of their accelerations: 
a_joan / a_sally = [2 * (d / (t-50s)) / (t-50s)] / [2d / (300 s)^2] 
a_joan / a_sally = [300^2 / (t-50s)^2] * [(d / (t-50s)) / d] 
a_joan / a_sally = [300^2 / (t-50s)^2] * (1 / (t-50s))

Plugging in the values: 
a_joan / a_sally = [300^2 / (250s)^2] * (1 / 250s) 
a_joan / a_sally = 1.44

Quiz 2: Motion in One Dimension

The position of an object at equal time intervals is shown below: Which graph below correctly represents position versus time for this object?

Five motion diagrams in which points represent the positions of an object at equal time intervals are shown below. Which statement is correct?

Driver A is cruising along enjoying the autumn colours. Driver B starts her car at the instant he passes her. Their velocities are shown as functions of time in the graph below. At what instants in time on the graph are drivers A and B side by side?

Two identical balls are at rest side by side at the bottom of a hill. Some time after ball A is kicked up the hill, ball B is given a kick up the hill. Ball A is headed downhill when it passes ball B headed up the hill. At the instant when ball A passes ball B,

A skier leaves a ski jump with a horizontal velocity of 29.4 m/s. The instant before she lands three seconds later, the magnitudes of the horizontal and vertical components of her velocity are:

The small circles in the diagram below represent the positions along the x axis of a body at equal time intervals. Assume the body moves in a straight line. This diagram is most likely to describe:

Jane says that any change in velocity is directly proportional to the time interval over which the change took place. Dana says that is true only when the acceleration is constant. Which one, if either, is correct?

The area under a graph of ax vs t from t = ti to t = tf represents:

The speed of an object is given by $v=5.00 t^{2}+4.00 t$ where v is in m/s and t is in s. What is the acceleration of the object at t = 2.00 s?

Two children start at one end of a street, the origin, run to the other end, then head back. On the way back Joan is ahead of Mike. At this moment in time, which statement is correct about the distances run and the displacements from the origin?

A particle moving along the x axis has a position given by x = 54t - 2.0t3 m. At the time t = 3.0 s, the speed of the particle is zero. Which statement is correct?

To help Kim practice for the Paralympics, Sally runs beside him for half the required distance. She runs the remaining distance at her regular speed and arrives 90 seconds ahead of Kim. What is the ratio of Sally's regular speed to Kim's speed? Use tKim for Kim's total time.

The graph below shows the velocity versus time graph for a ball. Which explanation best fits the motion of the ball as shown by the graph?

The equation that solves a problem is $\left(18 \frac{\mathrm{~m}}{\mathrm{~s}}\right) ^{2}-\left(0 \frac{\mathrm{~m}}{\mathrm{~s}}\right) ^{2}=2\left(3.0 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}\right) (3.0 \mathrm{~m})$ . The problem is:

The position of a particle moving along the y axis has a position given by: $y=0.20 \mathrm{~m}+\left(8.0 \frac{\mathrm{~m}}{\mathrm{~s}}\right) t-\left(10 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}\right) \mathrm{t}^{2}$ Is there any time interval during which the particle is not moving?

A boy on a skate board skates off a horizontal bench at a velocity of 10 m/s. One tenth of a second after he leaves the bench, to two significant figures, the magnitudes of his velocity and acceleration are:

In 20 minutes, Lucy ran 2.40 km on a treadmill facing due east. Relative to the gym, what were her displacement and average velocity during this time interval?

When starting from rest at the bottom of a straight road with constant upward slope, Joan bicycles to the top 50.0 s ahead of Sally, whose travel time is 5.00 minutes. What is the ratio of Joan's acceleration to Sally's acceleration?