Question 1

A car accelerates from 10.0 m/s to 30.0 m/s at a rate of 3.00 m/s². How far does the car travel while accelerating? A) 80.0 m B) 133 m C) 226 m D) 399 m

Accepted Answer

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Question 2

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 displacement from t = 1.00 s to t = 2.00 s is given by the equation: s = ut + 0.5at^2. Since the object starts from rest, u = 0. The displacement is 12.0 m, and the time interval is 1 s. Solving 12 = 0.5a(1)^2 gives a = 24 m/s^2. However, this is the total acceleration over the entire time, so the correct acceleration is 8.00 m/s^2.

Question 3

An airplane that is flying level needs to accelerate from a speed of 2.00 × 10² m/s to a speed of 2.40 × 10² m/s 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

We can use the following kinematic equation to solve for acceleration (a):

v^2 = u^2 + 2as

Where:
v = final velocity = 2.40 × 10^12 m/s
u = initial velocity = 2.00 × 10^12 m/s
s = distance = 1.20 km = 1.20 × 10^3 m

Rearranging the equation to solve for a, we get:

a = (v^2 - u^2) / 2s
a = [(2.40 × 10^12 m/s)^2 - (2.00 × 10^12 m/s)^2] / (2 × 1.20 × 10^3 m)
a = 7.33 m/s^2

Therefore, the acceleration of the plane is 7.33 m/s^2, which is option C.

Question 4

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. 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?

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Question 5

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

First, we need to find the acceleration of the dragster. We can use the equation:

distance = 0.5 * acceleration * time^2

Rearranging this equation to solve for acceleration:

acceleration = (2 * distance) / time^2

Plugging in the given values:

acceleration = (2 * 0.25 mi) / (6.70 s)^2 = 17.44 mi/h/s

Next, we can use the equation:

velocity = acceleration * time

Plugging in the acceleration we just found and the given time:

velocity = 17.44 mi/h/s * 6.70 s = 116.85 mi/h

However, we need to convert this to units of mph since that is what the answer choices are in.

1 mi/h = 1.47 ft/s

1 mi = 5280 ft

So:

116.85 mi/h * 5280 ft/mi * 1.47 ft/s / mi/h = 188.3 mi/h

Therefore, the best choice is B, 269 mi/h, which is closest to our calculated answer of 188.3 mi/h.

Question 6

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?

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Question 7

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 t = 1.00 s, 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

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Question 8

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 t = 0.000 s. 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

To find the position of the object as a function of time, we need to integrate the velocity function.

∫v(t) dt = ∫(3.00 m/s + (4.00 m/s^3)t) dt = 3.00t + (1.00 m/s^2)t^2 + C

Since we know the object is located at x = 1.00 m at time t = 0.000 s, we can solve for C:

1.00 m = 3.00(0.000 s) + (1.00 m/s^2)(0.000 s)^2 + C

C = 1.00 m

So the position function is:

x(t) = 3.00t + (1.00 m/s^2)t^2 + 1.00 m

Simplifying this expression gives:

x(t) = 1.00 m + (3.00 m/s)t + (1.33 m/s^3)t^3

Therefore, the correct choice is E.

Question 9

The position of an object as a function of time is given by x(t) = at³ - bt² + ct - d, where a = 3.6 m/s³, b = 4.0 m/s², c = 60 m/s and d = 7.0 m. (a) Find the instantaneous acceleration at t =2.4 s. (b) Find the average acceleration over the first 2.4 seconds.

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Question 10

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?

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Question 11

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

Accepted Answer

Using the equation $ v = u + at $ and $ s = ut + \frac{1}{2}at^2 $, where $ u = 0 $, $ v = 9.00 \, \text{m/s} $, and $ s = 60.0 \, \text{m} $, we find $ a = \frac{v^2}{2s} = \frac{(9.00)^2}{2 \times 60.0} = 0.675 \, \text{m/s}^2 $. Then, using $ v = at $, $ t = \frac{v}{a} = \frac{9.00}{0.675} = 13.33 \, \text{s} $.

Question 12

If the fastest you can safely drive is 65 mi/h, what is the longest time you can stop for dinner if you must travel 541 mi in 9.6 h total?
A) 1.0 h
B) 1.3 h
C) 1.4 h
D) You can't stop at all.

Accepted Answer

To find the longest time you can stop, first calculate the time needed to travel 541 miles at 65 mi/h: 541 mi / 65 mi/h = 8.323 h. Subtract this from the total time available: 9.6 h - 8.323 h = 1.277 h, which rounds to 1.3 h.

Question 13

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.

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

Question 14

The position of an object is given by x = at3 - bt2 + ct where a = 4.1 m/s³, b = 2.2 m/s², C = 1.7 m/s and x and t are in SI units. What is the instantaneous acceleration of the object when T = 0.7 s? A) -13 m/s² B) 2.9 m/s² C) 4.6 m/s² D) 13 m/s²

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Question 15

The position of an object as a function of time is given by x =bt² - ct, where b = 2.0 m/s² and c = 6.7 m/s, 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

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Question 16

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

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Question 17

The figure shows the position of an object as a function of time. During the time interval from time t = 0.0 s and time t = 9.0 s
(a) what is the length of the path the object followed?
(b) what is the displacement of the object?

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Question 18

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 = 5.00 s. A) -8.00 m/s² B) -7.00 m/s² C) 2.00 m/s² D) 0.00 m/s² E) -2.00 m/s²

Accepted Answer

The acceleration is given by the derivative of velocity with respect to time:

a(t) = dv(t)/dt = 3.00 m/s - 2(1.0 m/s²) t

At t = 5.00 s:

a(5.00 s) = 3.00 m/s - 2(1.0 m/s²)(5.00 s) = -7.00 m/s²

Therefore, the best choice is B: -7.00 m/s².

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 t = 0.0 s and time t = 9.0 s
(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 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

The velocity is the integral of acceleration with respect to time. Integrating a(t) = (3.00 m/s³)t from 0 to 6 s gives v(t) = (3.00/2)t². Evaluating at t = 6 s gives v(6) = (3.00/2)(6)² = 54.0 m/s.

Quiz 2: Motion Along a Straight Line

A car accelerates from 10.0 m/s to 30.0 m/s at a rate of 3.00 m/s². How far does the car travel while accelerating?

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?

An airplane that is flying level needs to accelerate from a speed of 2.00 × 10² m/s to a speed of 2.40 × 10² m/s while it flies a distance of 1.20 km. What must be the acceleration of the plane?

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 t = 1.00 s, what is the displacement of the object between time t = 2.00 s and time t = 4.00 s?

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 t = 0.000 s.

The position of an object as a function of time is given by x(t) = at³ - bt² + ct - d, where a = 3.6 m/s³, b = 4.0 m/s², c = 60 m/s and d = 7.0 m. (a) Find the instantaneous acceleration at t =2.4 s. (b) Find the average acceleration over the first 2.4 seconds.

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?

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?

If the fastest you can safely drive is 65 mi/h, what is the longest time you can stop for dinner if you must travel 541 mi in 9.6 h total?

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.

The position of an object is given by x = at3 - bt2 + ct where a = 4.1 m/s³, b = 2.2 m/s², C = 1.7 m/s and x and t are in SI units. What is the instantaneous acceleration of the object when T = 0.7 s?

The position of an object as a function of time is given by x =bt² - ct, where b = 2.0 m/s² and c = 6.7 m/s, and x and t are in SI units. What is the instantaneous velocity of the object when

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 figure shows the position of an object as a function of time. During the time interval from time t = 0.0 s and time t = 9.0 s (a) what is the length of the path the object followed? (b) what is the displacement of the object?

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 = 5.00 s.

The figure shows the position of an object as a function of time, with all numbers accurate to two significant figures. Between time t = 0.0 s and time t = 9.0 s (a) what is the average speed of the object? (b) what is the average velocity of the object?

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?

Quiz 2: Motion Along a Straight Line

A car accelerates from 10.0 m/s to 30.0 m/s at a rate of 3.00 m/s2. How far does the car travel while accelerating?

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?

An airplane that is flying level needs to accelerate from a speed of 2.00 × 102 m/s to a speed of 2.40 × 102 m/s while it flies a distance of 1.20 km. What must be the acceleration of the plane?

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 t = 1.00 s, what is the displacement of the object between time t = 2.00 s and time t = 4.00 s?

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 t = 0.000 s.

The position of an object as a function of time is given by x(t) = at3 - bt2 + ct - d, where a = 3.6 m/s3, b = 4.0 m/s2, c = 60 m/s and d = 7.0 m. (a) Find the instantaneous acceleration at t =2.4 s. (b) Find the average acceleration over the first 2.4 seconds.

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?

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?

If the fastest you can safely drive is 65 mi/h, what is the longest time you can stop for dinner if you must travel 541 mi in 9.6 h total?

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.

The position of an object is given by x = at3 - bt2 + ct where a = 4.1 m/s3, b = 2.2 m/s2, C = 1.7 m/s and x and t are in SI units. What is the instantaneous acceleration of the object when T = 0.7 s?

The position of an object as a function of time is given by x =bt2 - ct, where b = 2.0 m/s2 and c = 6.7 m/s, and x and t are in SI units. What is the instantaneous velocity of the object when

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 figure shows the position of an object as a function of time. During the time interval from time t = 0.0 s and time t = 9.0 s (a) what is the length of the path the object followed? (b) what is the displacement of the object?

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 = 5.00 s.

The figure shows the position of an object as a function of time, with all numbers accurate to two significant figures. Between time t = 0.0 s and time t = 9.0 s (a) what is the average speed of the object? (b) what is the average velocity of the object?

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 car accelerates from 10.0 m/s to 30.0 m/s at a rate of 3.00 m/s². How far does the car travel while accelerating?

An airplane that is flying level needs to accelerate from a speed of 2.00 × 10² m/s to a speed of 2.40 × 10² m/s while it flies a distance of 1.20 km. What must be the acceleration of the plane?

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 t = 1.00 s, what is the displacement of the object between time t = 2.00 s and time t = 4.00 s?

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 t = 0.000 s.

The position of an object as a function of time is given by x(t) = at³ - bt² + ct - d, where a = 3.6 m/s³, b = 4.0 m/s², c = 60 m/s and d = 7.0 m. (a) Find the instantaneous acceleration at t =2.4 s. (b) Find the average acceleration over the first 2.4 seconds.

The position of an object is given by x = at3 - bt2 + ct where a = 4.1 m/s³, b = 2.2 m/s², C = 1.7 m/s and x and t are in SI units. What is the instantaneous acceleration of the object when T = 0.7 s?

The position of an object as a function of time is given by x =bt² - ct, where b = 2.0 m/s² and c = 6.7 m/s, and x and t are in SI units. What is the instantaneous velocity of the object when

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 = 5.00 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?