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AP Physics C: Mech

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Unit 1

1.4 MC Answers and Review

8 min read•december 26, 2021

AP Physics C: Mechanics ⚙️

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Answers and Review for Multiple Choice Practice on Kinematics

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⛔STOP!⛔ Before you look at the answers make sure you gave this practice quiz a try so you can assess your understanding of the concepts covered in unit 1. Click here for the practice questions: AP Physics C: Mech Unit 1 Multiple Choice Questions.

Facts about the test: The AP Physics C: Mechanics exam has 35 multiple choice questions and you will be given 45 minutes to complete the section. That means it should take you around 20 minutes to complete 15 questions.

*The following questions were not written by CollegeBoard and although they cover information outlined in the AP Physics C: Mechanics Course and Exam Description the formatting on the exam may be different.

1. Two objects are released off of a building from the same height. Object A is dropped and hits the ground in time t. Object B is thrown upward with a velocity of v0 and hits the ground in a time 3t. Assume air resistance is negligible, write an expression for v0.

A. 13.1t

B. 16.3t

C. 4.9t^2

D. 49t^2 + 3t

Answer: Use the kinematics equation x = x0 + v0t + (1/2)at^2 to write an expression for each object. Recognizing that the final position of each object is the same, you can set the expressions each to each other and solve for v0.

📄 Study AP Physics C: Mech, Unit 1.1: Motion in One Dimension

2. The speed of a toy car moving on a straight track is given by the following equation: v = 0.5(t^2) + 4t. In this equation, velocity is in centimeters per second and time is in seconds. What is the acceleration of the toy car at t = 5 seconds?

A. 9 cm/s^2

B. 18 cm/s^2

C. 32.5 cm/s^2

D. 71 cm/s^2

Answer: Take the derivative of the velocity function to find the expression for acceleration to be a = t + 4. Then, plug in 5 seconds for t.

📄 Study AP Physics C: Mech, Unit 1.1: Motion in One Dimension

3. An object’s velocity is described by the function v = 2kt m/s, where t is in seconds and k is a constant. The object’s position is x = 58m when t = 4s. At t = 0s, the object is at x = 10m. What is the value of k?

A. 2

B. 3

C. 3.6

D. 12

Answer: Integrate the velocity function to get a position function of x = k(t^2) + c. Put in the initial conditions to get x = k(t^2) + 10. Plugin 58m and 4s to solve for k.

📄 Study AP Physics C: Mech, Unit 1.1: Motion in One Dimension

4. A cannonball is shot vertically upward with a positive initial velocity. At the max height of the cannonball, which of the following statements are true? Air resistance is negligible.

A. The acceleration of the cannonball is positive.

B. The velocity of the cannonball is positive.

C. The velocity of the cannonball is negative.

D. The acceleration of the cannonball is negative.

Answer: At the max height, the velocity of the cannonball is zero, so neither positive nor negative. Since air resistance is negligible, the only force acting on the cannonball is gravity, so the cannonball's acceleration is -9.81 m/s^2 and is therefore negative.

📄 Study AP Physics C: Mech, Unit 1.1: Motion in One Dimension

5. A Tesla Model S accelerates from 0 mph to 60 mph in 2.4 seconds. Assuming a constant acceleration, how far long does it take for a Tesla to reach 100 mph?

A. 3.2 seconds

B. 4 seconds

C. 4.8 seconds

D. 5.4 seconds

Answer: Use the kinematics equation v = v0 + at to find that the Tesla's acceleration is 25 mph/s. Then, reuse that same equation plugging in 100 mph for v and 25 mph/s for a to find t = 4 seconds.

📄 Study AP Physics C: Mech, Unit 1.1: Motion in One Dimension

6. A paddle boat driver is trying to go east across a river to get directly to the other side. The paddle boat driver can travel at a max speed of 5 m/s, and the river flows at a rate of 2m/s north to south. At what angle should the paddle boat point in order to land directly across the river?

A. 23.6 degrees

B. 66.4 degrees

C. 156.4 degrees

D. 203.6 degrees

Answer: Use vector addition to take into account the relative motion of the stream. The driver must aim her boat upstream. Using the boat's velocity as the hypotenuse of the triangle, solve for the angle upstream.

📄 Study AP Physics C: Mech, Unit 1.1: Motion in One Dimension

7. A physics student rolls a ball horizontally from a second floor classroom window that is 20 meters off of the ground. What is an appropriate expression for the range of the ball?

A. v0

B. 0.5v0

C. 2v0

D. 2v0 + 19.6

Answer: First, solve for the time it takes the ball to hit the ground using information in the y direction. Assuming the initial velocity in the y direction is zero, the ball takes 2 seconds to hit the ground. Then, plug into x = x0 + v0(t) + (1/2)at^2 with the acceleration as zero.

📄 Study AP Physics C: Mech, Unit 1.2: Motion in Two Dimensions

8. A helicopter drops a relief package as it moves with a constant horizontal velocity v. Assuming there is no air resistance, where is the package relative to the helicopter when it hits the ground?

A. Directly below the helicopter

B. Behind the helicopter

C. In front of the helicopter

D. Not enough information to tell

Answer: Since there is no air resistance, the package continues with the same horizontal velocity that it started with as it was dropped from the helicopter. Motion in the x direction is independent of motion in the y direction.

📄 Study AP Physics C: Mech, Unit 1.1: Motion in One Dimension

9. The x- and y- coordinates of a particle in motion, as a function of time, are given:

x = t^2 - t + 1 and y = t^3 -2(t^2) - 3.

What is the magnitude of the particle's velocity at 2 seconds?

A. 3 m/s

B. 4 m/s

C. 4.25 m/s

D. 5 m/s

Answer: First, take the derivative of each position function to find the component velocity functions. Then, plug in 2 seconds to get the component velocities. Finally, use vector addition to find the resultant velocity (it's a 3-4-5 triangle!)

📄 Study AP Physics C: Mech, Unit 1.1: Motion in One Dimension

10. A daredevil is launched with an initial velocity of 8 meters per second from the ground level at an angle of 37° above the horizontal. What are the horizontal and vertical components of the daredevil’s velocity as it is launched? Assume no air resistance.

A. Horizontal = 0.08 m/s, Vertical = 0.1 m/s

B. Horizontal = 6.4 m/s, Vertical = 4.8 m/s

C. Horizontal = 4.8 m/s, Vertical = 6.4 m/s

D. Horizontal = 8m/s, Vertical = 8 m/s

Answer: Use right triangle trig to find the horizontal and vertical components of the velocity. Use 8 as the hypotenuse of the triangle, and solve 8sin(37) = 4.8 for the vertical component and 8cos(37) = 6.4 for the horizontal component.

📄 Study AP Physics C: Mech, Unit 1.2: Motion in Two Dimensions

11. A ball is launched with an initial velocity of 4 m/s off of a 100 meter tall building at an angle of 53° above the horizontal. What are the horizontal and vertical components of the ball's velocity at its maximum height? Assume no air resistance.

A. Horizontal = 0 m/s, Vertical = 3.2 m/s

B. Horizontal = 2.4 m/s, Vertical = 0 m/s

C. Horizontal = 2.4 m/s, Vertical = 3.2 m/s

D. Horizontal = 4 m/s, Vertical = 0 m/s

Answer: At the max height, the velocity of the cannonball in the vertical direction is zero. The velocity in the horizontal direction stays constant, so find the x component of the initial velocity using the expression 4cos(53). The 100 meter building is irrelevant.

📄 Study AP Physics C: Mech, Unit 1.2: Motion in Two Dimensions

12. The x and y components of an object's acceleration are given in the functions below:

ax = -2t + 6 and ay = 4t

Assuming that the object's initial velocity was zero, find the magnitude of the object's velocity at t = 2 seconds.

A. 8*sqrt(2) m/s

B. 8 m/s

C. 8.25 m/s

D. 64 m/s

Answer: Integrate each acceleration function to get velocity functions in the x and y direction. The "c" value in your integration becomes 0 because the initial velocity was zero. Then, plug in 2 seconds for each expression and add component velocities.

📄 Study AP Physics C: Mech, Unit 1.1: Motion in One Dimension

13. A car accelerates in a straight line modeled by the function a = -8t. At time t = 0 m/s, the car’s velocity is 20 m/s in the positive direction. At what time is the car’s instantaneous velocity equal to zero?

A. 0 seconds

B. 1.32 seconds

C. 2.24 seconds

D. 5 seconds

Answer: Integrate the acceleration function to find the velocity function, making sure to account for the car's 20 m/s initial velocity. Then, plug in 0 for the velocity of the car and solve for t.

📄 Study AP Physics C: Mech, Unit 1.1: Motion in One Dimension

14. A physics student rolls a ball off of a 30m building in the direction of the target that lies flat on the ground. If the target is 16 m from the side of the building, and air resistance is negligible, with what horizontal speed must the ball leave the top of the building if it is to land on the target?

A. 6.5 m/s

B. 9.2 m/s

C. 40 m/s

D. 97.8 m/s

Answer: Use the kinematic equations to solve this problem, remembering that x and y directions are independent. First, use the information in the vertical direction to solve for the time the ball falls and hits the ground. Then, use the time you solved for in order to find the initial velocity in the x direction.

📄 Study AP Physics C: Mech, Unit 1.2: Motion in Two Dimensions

15. Assuming no air resistance, an object dropped on Earth experiences a constant acceleration of about -9.8m/s^2. Which of the following statements are true?

A. This means that the object’s velocity as it falls is 9.8 m/s.

B. This means that the object covers 9.8 m each second that it falls.

C. This means that the object covers 9.8 meters during the first second of its fall.

D. This means that the velocity of the object increases 9.8 m/s each second as it falls towards the Earth.

Answer: Acceleration is defined as the change in velocity of an object. If an object falls at 9.8 m/s/s, it's velocity is increasing by 9.8 m/s each second that it falls. The position of the object is not a linear relationship, and the velocity changes throughout the fall.

📄 Study AP Physics C: Mech, Unit 1.1: Motion in One Dimension

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🚗Unit 1 – Kinematics

1.1Kinematics Overview and Motion in One Dimension

1.2Kinematics: Motion in Two Dimensions

1.3Multiple Choice Questions

1.4MC Answers and Review