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100+ Free AP Physics C: Mechanics Practice Questions

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On a velocity-versus-time graph, a straight line with negative slope crossing zero represents an object that is:

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B
C
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Key Facts: AP Physics C: Mechanics Exam

40

multiple-choice questions in 80 minutes, worth 50% of the score

College Board AP Central

4

free-response questions in 100 minutes, worth 50% of the score

College Board AP Central

7

units, from kinematics to oscillations, in the redesigned framework

College Board CED 2024

1-5

score scale, with 3 or higher typically earning college credit

College Board

May 2025

first administration of the redesigned exam format

AP Physics Revisions 2024-25

$99

approximate US exam fee per AP exam for 2025-26

College Board

AP Physics C: Mechanics is a calculus-based mechanics exam scored 1-5, with a 3 or higher typically earning college credit. After the 2024-25 redesign first given in May 2025, Section I has 40 multiple-choice questions in 80 minutes (now with four answer choices each, up from 35 questions with five choices) and Section II has 4 free-response questions in 100 minutes; each section is 50% of the score. A calculator and an official equation sheet are permitted on both sections, and the total exam time is 3 hours (source: College Board, apcentral.collegeboard.org).

Sample AP Physics C: Mechanics Practice Questions

Try these sample questions to test your AP Physics C: Mechanics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A particle moves along the x-axis with position given by x(t) = 3t^3 - 2t^2 + 5 (SI units). What is the particle's acceleration at t = 2 s?
A.32 m/s^2
B.28 m/s^2
C.36 m/s^2
D.20 m/s^2
Explanation: Velocity is the first derivative: v(t) = 9t^2 - 4t. Acceleration is the second derivative: a(t) = 18t - 4. At t = 2 s, a = 18(2) - 4 = 32 m/s^2. Differentiating position twice is the core calculus relationship in kinematics.
2A ball is thrown straight up with an initial speed of 20 m/s. Taking g = 10 m/s^2 and neglecting air resistance, how high does it rise above the launch point?
A.10 m
B.20 m
C.40 m
D.60 m
Explanation: At the highest point the velocity is zero. Using v^2 = v0^2 - 2g(h), 0 = (20)^2 - 2(10)h, so h = 400/20 = 20 m. This is a standard one-dimensional kinematics result for vertical motion.
3A projectile is launched at 30 m/s at an angle of 30 degrees above the horizontal. Taking g = 10 m/s^2, what is the horizontal range on level ground?
A.45 m
B.90 m
C.78 m
D.52 m
Explanation: Range R = (v0^2 sin(2theta))/g = (30^2 * sin 60)/10 = (900 * 0.866)/10 = 77.9 m, about 78 m. The sin(2theta) form follows from combining horizontal and vertical projectile motion.
4The velocity of an object is given by v(t) = 4t (SI units), starting from x = 0 at t = 0. What is the displacement during the first 3 seconds?
A.12 m
B.36 m
C.24 m
D.18 m
Explanation: Displacement is the integral of velocity: x = integral of 4t dt from 0 to 3 = 2t^2 evaluated from 0 to 3 = 2(9) = 18 m. The area under the velocity-time graph gives displacement.
5Two objects are dropped from rest, the second one second after the first, from the same height. As they fall (neglecting air resistance), what happens to the vertical distance between them?
A.It increases
B.It stays constant
C.It decreases
D.It first increases then decreases
Explanation: Both accelerate at g, but the first object always has a greater speed because it has been falling longer. Since the leading object moves faster at every instant, the gap between them grows continuously with time.
6A car accelerates uniformly from rest, covering 100 m in 5 s. What is its acceleration?
A.4 m/s^2
B.8 m/s^2
C.20 m/s^2
D.10 m/s^2
Explanation: Using x = (1/2)a t^2 with x = 100 m and t = 5 s: 100 = (1/2)a(25), so a = 200/25 = 8 m/s^2. This is the standard constant-acceleration relationship starting from rest.
7On a velocity-versus-time graph, a straight line with negative slope crossing zero represents an object that is:
A.Speeding up the entire time in the positive direction
B.Moving at constant velocity
C.Decelerating, momentarily stopping, then speeding up in the opposite direction
D.At rest the entire time
Explanation: A constant negative slope means constant negative acceleration. While velocity is positive and decreasing the object slows; at the zero crossing it momentarily stops; then velocity becomes negative and increasing in magnitude, so it speeds up in the opposite direction.
8A particle's acceleration is a(t) = 6t (SI units). If it starts from rest at the origin, what is its velocity at t = 2 s?
A.8 m/s
B.6 m/s
C.24 m/s
D.12 m/s
Explanation: Velocity is the integral of acceleration: v(t) = integral of 6t dt = 3t^2 (with v(0) = 0). At t = 2 s, v = 3(4) = 12 m/s. Integrating acceleration recovers velocity given the initial condition.
9A projectile is launched horizontally from a height of 45 m at 20 m/s. Taking g = 10 m/s^2, how far horizontally does it travel before landing?
A.60 m
B.45 m
C.90 m
D.20 m
Explanation: Time to fall: 45 = (1/2)(10)t^2, so t^2 = 9 and t = 3 s. Horizontal distance = (20 m/s)(3 s) = 60 m. Horizontal and vertical motions are independent in projectile problems.
10An object moving in the +x direction has a constant negative acceleration. Which statement must be true?
A.Its speed is increasing
B.Its speed is decreasing while it moves in +x
C.It is at rest
D.Its displacement is zero
Explanation: When velocity and acceleration point in opposite directions, the object slows down. With positive velocity and negative acceleration, the speed decreases while the object continues moving in the +x direction until it possibly reverses.

About the AP Physics C: Mechanics Exam

AP Physics C: Mechanics is a calculus-based, college-level introductory mechanics course administered by the College Board. Following the 2024-25 redesign (first administered May 2025), the exam has a multiple-choice Section I of 40 questions in 80 minutes and a free-response Section II of 4 questions in 100 minutes, each worth 50% of the score. The course is organized into seven units spanning kinematics, dynamics, energy, momentum, rotation, and oscillations.

Questions

40 scored questions

Time Limit

3 hours (80 min multiple-choice + 100 min free-response)

Passing Score

Scored 1-5; a 3 or higher typically earns college credit

Exam Fee

About $99 per exam (2025-26) (College Board)

AP Physics C: Mechanics Exam Content Outline

10-15%

Unit 1: Kinematics

Position, velocity, and acceleration in one and two dimensions, motion graphs, projectile motion, and calculus relations among kinematic quantities.

20-25%

Unit 2: Force and Translational Dynamics

Newton's three laws, free-body diagrams, friction, springs, gravitation, uniform circular motion, and resistive (drag) forces.

15-25%

Unit 3: Work, Energy, and Power

Work as the line integral of force, work-energy theorem, kinetic and potential energy, conservation of energy, and power.

10-20%

Unit 4: Linear Momentum

Impulse-momentum theorem, conservation of linear momentum, elastic and inelastic collisions, and center of mass.

10-15%

Unit 5: Torque and Rotational Dynamics

Rotational kinematics, torque, moment of inertia, the rotational form of Newton's second law, and rotational statics.

10-15%

Unit 6: Energy and Momentum of Rotating Systems

Rotational kinetic energy, angular momentum and its conservation, rolling without slipping, and gravitational orbits.

10-15%

Unit 7: Oscillations

Simple harmonic motion, mass-spring systems, the simple pendulum, period and frequency, and energy in oscillating systems.

How to Pass the AP Physics C: Mechanics Exam

What You Need to Know

  • Passing score: Scored 1-5; a 3 or higher typically earns college credit
  • Exam length: 40 questions
  • Time limit: 3 hours (80 min multiple-choice + 100 min free-response)
  • Exam fee: About $99 per exam (2025-26)

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

AP Physics C: Mechanics Study Tips from Top Performers

1Master the calculus links first: velocity is the derivative of position, acceleration is the derivative of velocity, and displacement, work, and impulse are integrals - many MC questions test exactly these relationships.
2Memorize the standard moments of inertia (solid sphere 2/5 MR^2, solid disk/cylinder 1/2 MR^2, hoop MR^2, rod about center 1/12 ML^2) since the equation sheet gives only the general integral form.
3Always start dynamics problems with a clear free-body diagram before writing Newton's second law along each axis.
4Use conservation laws (energy, momentum, angular momentum) as shortcuts - they often avoid messy force-and-time analysis on collision and rotation problems.
5Practice with the official equation sheet so you know what is provided and what you must derive, and time yourself at about two minutes per multiple-choice question.

Frequently Asked Questions

How many questions are on the AP Physics C: Mechanics exam in 2026?

Section I has 40 multiple-choice questions (80 minutes, 50% of the score) and Section II has 4 free-response questions (100 minutes, 50%). This format reflects the 2024-25 redesign first administered in May 2025.

What changed in the 2024-25 AP Physics C: Mechanics redesign?

The multiple-choice section grew from 35 questions in 45 minutes to 40 questions in 80 minutes, answer choices were standardized to four options instead of five, and any learning objective can now be paired with any science practice. The seven-unit framework also reorganizes rotation and gravitation content.

Is AP Physics C: Mechanics calculus-based?

Yes. AP Physics C: Mechanics is calculus-based and assumes students are taking or have taken calculus. You use derivatives and integrals to relate position, velocity, and acceleration and to compute work, impulse, and other quantities.

Can I use a calculator and equation sheet on the exam?

Yes. A calculator is permitted on both the multiple-choice and free-response sections, and the College Board provides an official equation sheet (the table of information and equations) both in print and within the Bluebook app.

How is AP Physics C: Mechanics scored and what counts as passing?

The exam is scored on a 1-5 scale. A score of 3 is considered qualified and many colleges grant credit for a 3 or higher, though selective institutions may require a 4 or 5.

How much does the AP Physics C: Mechanics exam cost?

The standard AP exam fee in the United States is about $99 per exam for 2025-26. Fee reductions are available for eligible students, and schools may add or cover administrative costs.