Question 1

The velocity of an object is given by the expression v(t) = 3.00 m/s + (4.00 m/s³)t², where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time . A) (4.00 m/s)t + 1.00 m B) (3.00 m/s)t + (1.33 m/s3)t³ C) (4.00 m/s)t D) 1.33 m E) 1.00 m + (3.00 m/s)t + (1.33 m/s³)t³

Accepted Answer

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Question 2

A dragster starts from rest and travels 1/4 mi in 6.70 s with constant acceleration. What is its velocity when it crosses the finish line?
A) 296 mi/h
B) 269 mi/h
C) 188 mi/h
D) 135 mi/h

Accepted Answer

Firstly, since the dragster starts from rest, its initial velocity is 0.

Next, we can use the equation:

distance = 1/2*acceleration*time^2 + initial velocity*time

Since we know the distance (1/4 mi), time (6.70 s), and initial velocity (0), we can solve for the acceleration:

1/4 = 1/2*acceleration*(6.70)^2

Solving for acceleration gives us:

acceleration = 0.1784 mi/s^2

Now, using the equation:

final velocity = acceleration*time + initial velocity

We can find the final velocity when it crosses the finish line:

final velocity = 0.1784 mi/s^2 * 6.70 s = 1.195 mi/s

Finally, we convert this velocity from miles per second to miles per hour:

1.195 mi/s * 3600 s/hr = 4300 mi/hr

Therefore, the correct answer is B) 269 mi/h (the closest choice to our calculated answer).

Question 3

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³)t, where t is in seconds. If the object has a velocity 1.00 m/s at time what is the displacement of the object between time t = 2.00 s and time t = 4.00 s? A) 33.0 m B) 30.0 m C) 36.0 m D) 27.0 m

Accepted Answer

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Question 4

If the fastest you can safely drive is  what is the longest time you can stop for dinner if you must travel  in  total?
A) 1.0 h
B) 1.3 h
C) 1.4 h
D) You can't stop at all.

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The answer of If the fastest you can safely drive...

Question 5

A runner maintains constant acceleration after starting from rest as she runs a distance of 60.0 m. The runner's speed at the end of the 60.0 m is 9.00 m/s. How much time did it take the runner to complete the 60.0 m distance?
A) 6.67 s
B) 15.0 s
C) 9.80 s
D) 10.2 s
E) 13.3 s

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Question 6

The velocity of an object as a function of time is given by v(t) = 2.00 m/s + (3.00 m/s) t - (1.0 m/s²) t². Determine the instantaneous acceleration of the object at time t = 4.00 s. A) -2.00 m/s² B) -5.00 m/s² C) 1.00 m/s² D) 0.00 m/s² E) -1.00 m/s²

Accepted Answer

Acceleration is the derivative of velocity with respect to time. Taking the derivative of v(t), we get: a(t) = d/dt[v(t)] = 3.00 m/s - 2.0 m/s² t Plugging in t = 4.00 s gives: a(4.00) = 3.00 m/s - 2.0 m/s² (4.00) = -5.00 m/s² Therefore, the instantaneous acceleration of the object at time t = 4.00 s is -5.00 m/s², or choice B.

Question 7

A racing car accelerates uniformly from rest along a straight track. This track has markers spaced at equal distances along it from the start, as shown in the figure. The car reaches a speed of 140 km/h as it passes marker 2. Where on the track was the car when it was traveling at 70 km/h? 
A) Before marker 1
B) At marker 1
C) Between marker 1 and marker 2

Accepted Answer

The answer of A racing car accelerates uniformly from rest...

Question 8

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³)t, where t is in seconds. If the object is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s? A) 18.0 m/s B) 54.0 m/s C) 0.00 m/s D) 15.0 m/s E) 108 m/s

Accepted Answer

To find the velocity at time t=6s, we need to integrate the acceleration function from 0s to 6s:
v(t) = ∫[0,6] a(t) dt = ∫[0,6] (3.00t) dt
v(t) = 1.5t^2 + C   (where C is the constant of integration)
Since the object is at rest at t=0, we know that the initial velocity is 0 m/s. Therefore, we can solve for C:
0 = 1.5(0)^2 + C 
C = 0 
Thus the velocity function is: v(t) = 1.5t^2 
The velocity at t=6s is:
v(6) = 1.5(6)^2 = 54.0 m/s
Therefore, the correct answer is B.

Question 9

The figure shows a graph of the velocity as a function of time for a basketball player traveling up and down the court in a straight-line path. For the 10 s shown on the graph, find
(a) the net displacement of the player.
(b) the total distance run by the player.

Accepted Answer

The answer of The figure shows a graph of the...

Question 10

A car accelerates from  to  at a rate of  How far does the car travel while accelerating?
A) 80.0 m
B) 133 m
C) 226 m
D) 399 m

Accepted Answer

The answer of A car accelerates from  to ...

Question 11

The position of an object as a function of time is given by  where    and  (a) Find the instantaneous acceleration at t =2.4 s.
(b) Find the average acceleration over the first 2.4 seconds.

Accepted Answer

The answer of The position of an object as a...

Question 12

Arthur and Betty start walking toward each other when they are 100 m apart. Arthur has a speed of  and Betty has a speed of  Their dog, Spot, starts by Arthur's side at the same time and runs back and forth between them at 5.0 m/s. By the time Arthur and Betty meet, what distance has Spot run?

Accepted Answer

The answer of Arthur and Betty start walking toward each...

Question 13

An airplane that is flying level needs to accelerate from a speed of 2.00 × 10² m/s to a speed of while it flies a distance of 1.20 km. What must be the acceleration of the plane? A) 4.44 m/s² B) 2.45 m/s² C) 7.33 m/s² D) 5.78 m/s² E) 1.34 m/s²

Accepted Answer

The answer of An airplane that is flying level needs...

Question 14

An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 12.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object? A) -12.0 m/s² B) 24.0 m/s² C) -4.00 m/s² D) 4.00 m/s² E) 8.00 m/s²

Accepted Answer

The answer of An object starts from rest at time...

Question 15

The position of an object as a function of time is given by x =  - ct, where b = 2.0 m/  and  and x and t are in SI units. What is the instantaneous velocity of the object when 
A) 1.7 m/s
B) 2.1 m/s
C) 2.3 m/s
D) 2.7 m/s

Accepted Answer

The answer of The position of an object as a...

Question 16

The position of an object is given by where and x and t are in SI units. What is the instantaneous acceleration of the object when A) -13 m/s² B) 2.9 m/s² C) 4.6 m/s² D) 13 m/s²

Accepted Answer

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Question 17

A cat runs along a straight line (the x-axis) from point A to point B to point C, as shown in the figure. The distance between points A and C is 5.00 m, the distance between points B and C is 10.0 m, and the positive direction of the x-axis points to the right. The time to run from A to B is 20.0 s, and the time from B to C is 8.00 s. As the cat runs along the x-axis between points A and C
(a) what is the magnitude of its average velocity?
(b) what is its average speed?

Accepted Answer

The answer of A cat runs along a straight line...

Question 18

The figure shows the position of an object as a function of time. During the time interval from time  and time  (a) what is the length of the path the object followed?
(b) what is the displacement of the object?

Accepted Answer

The answer of The figure shows the position of an...

Question 19

The figure shows the position of an object as a function of time, with all numbers accurate to two significant figures. Between time  and time  (a) what is the average speed of the object?
(b) what is the average velocity of the object?

Accepted Answer

The answer of The figure shows the position of an...

Question 20

The figure represents the position of a particle as it travels along the x-axis. Between t = 2 s and t = 4 s, what is (a) the average speed of the particle and (b) the average velocity of the particle?

Accepted Answer

The answer of The figure represents the position of a...

Quiz 2: Kinematics in One Dimension

The velocity of an object is given by the expression v(t) = 3.00 m/s + (4.00 m/s³) t², where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time .

A dragster starts from rest and travels 1/4 mi in 6.70 s with constant acceleration. What is its velocity when it crosses the finish line?

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³) t, where t is in seconds. If the object has a velocity 1.00 m/s at time what is the displacement of the object between time t = 2.00 s and time t = 4.00 s?

If the fastest you can safely drive is what is the longest time you can stop for dinner if you must travel in total?

A runner maintains constant acceleration after starting from rest as she runs a distance of 60.0 m. The runner's speed at the end of the 60.0 m is 9.00 m/s. How much time did it take the runner to complete the 60.0 m distance?

The velocity of an object as a function of time is given by v(t) = 2.00 m/s + (3.00 m/s) t - (1.0 m/s²) t². Determine the instantaneous acceleration of the object at time t = 4.00 s.

A racing car accelerates uniformly from rest along a straight track. This track has markers spaced at equal distances along it from the start, as shown in the figure. The car reaches a speed of 140 km/h as it passes marker 2. Where on the track was the car when it was traveling at 70 km/h?

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³) t, where t is in seconds. If the object is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s?

The figure shows a graph of the velocity as a function of time for a basketball player traveling up and down the court in a straight-line path. For the 10 s shown on the graph, find (a) the net displacement of the player. (b) the total distance run by the player.

A car accelerates from to at a rate of How far does the car travel while accelerating?

The position of an object as a function of time is given by where and (a) Find the instantaneous acceleration at t =2.4 s. (b) Find the average acceleration over the first 2.4 seconds.

Arthur and Betty start walking toward each other when they are 100 m apart. Arthur has a speed of and Betty has a speed of Their dog, Spot, starts by Arthur's side at the same time and runs back and forth between them at 5.0 m/s. By the time Arthur and Betty meet, what distance has Spot run?

An airplane that is flying level needs to accelerate from a speed of 2.00 × 10² m/s to a speed of while it flies a distance of 1.20 km. What must be the acceleration of the plane?

An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 12.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?

The position of an object as a function of time is given by x = - ct, where b = 2.0 m/ and and x and t are in SI units. What is the instantaneous velocity of the object when

The position of an object is given by where and x and t are in SI units. What is the instantaneous acceleration of the object when

The figure shows the position of an object as a function of time. During the time interval from time and time (a) what is the length of the path the object followed? (b) what is the displacement of the object?

The figure shows the position of an object as a function of time, with all numbers accurate to two significant figures. Between time and time (a) what is the average speed of the object? (b) what is the average velocity of the object?

The figure represents the position of a particle as it travels along the x-axis. Between t = 2 s and t = 4 s, what is (a) the average speed of the particle and (b) the average velocity of the particle?

Quiz 2: Kinematics in One Dimension

The velocity of an object is given by the expression v(t) = 3.00 m/s + (4.00 m/s3) t2, where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time .

A dragster starts from rest and travels 1/4 mi in 6.70 s with constant acceleration. What is its velocity when it crosses the finish line?

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s3) t, where t is in seconds. If the object has a velocity 1.00 m/s at time what is the displacement of the object between time t = 2.00 s and time t = 4.00 s?

If the fastest you can safely drive is what is the longest time you can stop for dinner if you must travel in total?

A runner maintains constant acceleration after starting from rest as she runs a distance of 60.0 m. The runner's speed at the end of the 60.0 m is 9.00 m/s. How much time did it take the runner to complete the 60.0 m distance?

The velocity of an object as a function of time is given by v(t) = 2.00 m/s + (3.00 m/s) t - (1.0 m/s2) t2. Determine the instantaneous acceleration of the object at time t = 4.00 s.

A racing car accelerates uniformly from rest along a straight track. This track has markers spaced at equal distances along it from the start, as shown in the figure. The car reaches a speed of 140 km/h as it passes marker 2. Where on the track was the car when it was traveling at 70 km/h?

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s3) t, where t is in seconds. If the object is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s?

The figure shows a graph of the velocity as a function of time for a basketball player traveling up and down the court in a straight-line path. For the 10 s shown on the graph, find (a) the net displacement of the player. (b) the total distance run by the player.

A car accelerates from to at a rate of How far does the car travel while accelerating?

The position of an object as a function of time is given by where and (a) Find the instantaneous acceleration at t =2.4 s. (b) Find the average acceleration over the first 2.4 seconds.

Arthur and Betty start walking toward each other when they are 100 m apart. Arthur has a speed of and Betty has a speed of Their dog, Spot, starts by Arthur's side at the same time and runs back and forth between them at 5.0 m/s. By the time Arthur and Betty meet, what distance has Spot run?

An airplane that is flying level needs to accelerate from a speed of 2.00 × 102 m/s to a speed of while it flies a distance of 1.20 km. What must be the acceleration of the plane?

An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 12.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?

The position of an object as a function of time is given by x = - ct, where b = 2.0 m/ and and x and t are in SI units. What is the instantaneous velocity of the object when

The position of an object is given by where and x and t are in SI units. What is the instantaneous acceleration of the object when

The figure shows the position of an object as a function of time. During the time interval from time and time (a) what is the length of the path the object followed? (b) what is the displacement of the object?

The figure shows the position of an object as a function of time, with all numbers accurate to two significant figures. Between time and time (a) what is the average speed of the object? (b) what is the average velocity of the object?

The figure represents the position of a particle as it travels along the x-axis. Between t = 2 s and t = 4 s, what is (a) the average speed of the particle and (b) the average velocity of the particle?

The velocity of an object is given by the expression v(t) = 3.00 m/s + (4.00 m/s³) t², where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time .

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³) t, where t is in seconds. If the object has a velocity 1.00 m/s at time what is the displacement of the object between time t = 2.00 s and time t = 4.00 s?

The velocity of an object as a function of time is given by v(t) = 2.00 m/s + (3.00 m/s) t - (1.0 m/s²) t². Determine the instantaneous acceleration of the object at time t = 4.00 s.

The acceleration of an object as a function of time is given by a(t) = (3.00 m/s³) t, where t is in seconds. If the object is at rest at time t = 0.00 s, what is the velocity of the object at time t = 6.00 s?

An airplane that is flying level needs to accelerate from a speed of 2.00 × 10² m/s to a speed of while it flies a distance of 1.20 km. What must be the acceleration of the plane?