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AP Physics C Mechanics Past Papers and Drilling: Calculus Kinematics, Rotation, SHM
TUTORZONE ORIGINAL DRILLING MOCK · AP PHYSICS C: MECHANICS
Written to the current College Board format: Section I multiple choice, 42 questions, 85 min, 50% (discrete + sets); Section II free response, 4 questions, 95 min, 50% (mathematical routines, translation between representations, experimental design, qualitative/quantitative). Calculators and an equation sheet are allowed. This drilling mock demonstrates 6 questions with answers and techniques.
What is in the AP Physics C: Mechanics exam?
Direct answer: the exam runs 3 hours: multiple choice 42 questions, 85 min, 50%; free response 4 questions, 95 min, 50%, across seven units.
Assessment at a glance (2027)
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Section II (Free Response) | 4: routines, representations, experiment, qualitative | 50% | 95 min |
| Section I (Multiple Choice) | 42: discrete + question sets | 50% | 85 min |
AP Physics C Mechanics drilling technique: v = dx/dt and a = dv/dt with displacement found by integration; variable-force work W = integral of F dx. Among the seven units, Force and Translational Dynamics carries 20-25% of the multiple-choice section and Work, Energy, and Power 15-25%. Always show integral, substitution and units.
How this paper was built
This is a TutorZone original drilling mock: the questions follow the College Board AP Physics C: Mechanics format and the answers are our own, not College Board past papers or marking references.
Every numeric answer was recomputed programmatically; the exam structure and unit weightings come from the official course and exam description.
The six questions cover six high-frequency locations: kinematics, variable-force work, impulse and momentum, rotation, simple harmonic motion and rolling.
Pacing
| Section | Marks | Suggested time | What to do first |
|---|---|---|---|
| Section II (Free Response) | 50% | about 24 min per question | write integral, substitute, units |
| Section I (Multiple Choice) | 50% | about 2 min per question | dimensional check and graph reasoning |
Which unit carries the most weight?
Direct answer: in the multiple-choice section, Force and Translational Dynamics carries 20-25% and Work, Energy, and Power 15-25%; kinematics, momentum, rotation and oscillations take 10-20% each.
Drilling (6 demonstrated)
Demonstrates calculus kinematics, variable-force work, impulse, moment of inertia, SHM and rolling without slipping.
Question 1 (8 marks)
A particle moves along the x-axis with v(t) = 3t^2 – 2t (m/s, t in seconds). Find the acceleration at t = 2 s and the displacement from t = 0 to 2 s.
Question 2 (8 marks)
A variable force F(x) = 6x (N) acts along the x-axis. Find the work done as the object moves from x = 0 to x = 2 m.
Question 3 (8 marks)
A 2 kg block at rest is pushed by F(t) = 4t (N) for 3 s. Find the impulse and the final speed.
Question 4 (8 marks)
A solid cylinder of mass 4 kg and radius 0.5 m spins about its central axis. A torque of 2 N m is applied. Find the moment of inertia and the angular acceleration.
Question 5 (8 marks)
A 200 N/m spring carries a 0.5 kg mass in simple harmonic motion. Find the angular frequency and the period.
Question 6 (8 marks)
A solid sphere rolls without slipping from rest down a 30 degree incline (g = 9.8 m/s^2). Find its linear acceleration.
Which topics does this paper drill?
Direct answer: calculus kinematics, variable-force work, impulse and momentum, moment of inertia, simple harmonic motion, and rolling without slipping.
Answers and marks per question
Question 1
a(t) = dv/dt = 6t – 2, so a(2) = 10 m/s^2 (4); displacement = integral of (3t^2 – 2t) dt from 0 to 2 = [t^3 – t^2] = 4 m (4).
Question 2
W = integral of 6x dx from 0 to 2 = [3x^2] = 12 J (8).
Question 3
Impulse J = integral of 4t dt from 0 to 3 = [2t^2] = 18 N s (4); v = J/m = 18 / 2 = 9 m/s (4).
Question 4
I = 0.5MR^2 = 0.5 x 4 x 0.25 = 0.5 kg m^2 (4); alpha = tau/I = 2 / 0.5 = 4 rad/s^2 (4).
Question 5
omega = sqrt(k/m) = sqrt(200 / 0.5) = 20 rad/s (4); T = 2 pi / omega = pi/10 s, about 0.31 s (4).
Question 6
Rolling without slipping: a = g sin(theta) / (1 + 2/5) = 9.8 x 0.5 / 1.4 = 3.5 m/s^2 (8). It is slower than a frictionless sliding block because some energy becomes rotational kinetic energy.
How much working must I show?
Direct answer: show the three layers – integral, substitution, units. Free-response marks are awarded by method, so an answer-only script loses most of the marks.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| No integral shown | Write 4 m only | No method marks | Show the integral of v dt |
| Wrong moment of inertia | Always I = MR^2 | A solid cylinder is 0.5MR^2 | Pick I by shape |
| Confusing omega with f | Treat 20 as Hz | Period comes out wrong | omega = 2 pi / T, T = pi/10 s |
How to use this paper
First drill: all 6 questions on the clock, equation sheet closed.
Mark it: check the three layers (integral, substitution, units) and the shape of I.
Second drill: redo three to seven days later, aiming to finish in under 40 minutes.
What should I do after drilling this paper?
Direct answer: log the questions where you skipped the integral or used the wrong I; redo the paper in three to seven days; then drill the AP Physics C E&M paper to cover electricity.
FAQ
Is this a College Board past paper?
No. The questions and answers are TutorZone originals, not College Board past papers or marking references.
What is in the AP Physics C: Mechanics exam?
3 hours: 42 multiple-choice questions in 85 min (50%) and 4 free-response questions in 95 min (50%), over seven units.
Are calculators allowed throughout?
Yes – both sections allow a calculator, and an equation sheet is provided.
Official references
| Resource | What to check |
|---|---|
| College Board AP Physics C: Mechanics exam page | Confirm the format, question counts and equation sheet |
| Official course and exam description (CED) | Check the seven-unit multiple-choice weightings |
| https://www.tutorzone.com.hk/en-ap-physics-1-mock-2027/ | AP Physics 1 drilling mock (algebra-based) |
| https://www.tutorzone.com.hk/en-ap-physics-c-electricity-and-magnetism-mock-2027/ | AP Physics C Electricity and Magnetism drilling mock |
Related: practice area · AP Physics 1 drilling mock · AP Physics C E&M drilling mock
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