AP Physics C: Mechanics — Practice Questions flashcards

6 of 50 questions free to study here · 7 topics · the whole deck is built into Willys

Multiple-choice practice questions, one best answer each, on calculus-based kinematics, drag, gravitation, work and potential energy, momentum, rotation and oscillations.

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Practice deck · part of AP Physics C: Mechanics · written against: College Board AP Physics C: Mechanics Course and Exam Description (2024 revision). Updated 2026-10-10.

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A particle moves along the x-axis with velocity $v(t) = 3t^2 - 12$ (m/s, t in seconds). At $t = 0$ it is at $x = 5$ m. Where is it at $t = 3$ s?

A) $x = -4$ m
B) $x = 12$ m
C) $x = -9$ m
D) $x = 20$ m

A) $x = -4$ m

Position is the starting point plus the integral of velocity: $x = 5 + \int_0^3 \left(3t^2 - 12\right) dt = 5 + \left(27 - 36\right) = -4$ m. Leaving out the initial position gives $-9$ m.
Kinematics
A thin rod lies along the x-axis from $x = 0$ to $x = L$ ⁠. Its linear mass density is $\lambda = Cx^2$ ⁠, where C is a positive constant. Where is its center of mass?

A) $x = \frac{2L}{3}$
B) $x = \frac{L}{2}$
C) $x = \frac{3L}{4}$
D) $x = \frac{L}{3}$

C) $x = \frac{3L}{4}$

$x_{cm} = \frac{\int x\lambda dx}{\int \lambda dx} = \frac{CL^4/4}{CL^3/3} = \frac{3L}{4}$ ⁠. The value $\frac{2L}{3}$ belongs to a density proportional to $x$ ⁠, not $x^2$ ⁠.
Force and Translational Dynamics › Center of Mass
A force along the x-axis is $F(x) = 12 - 3x^2$ (newtons, x in meters). How much work does it do on an object that moves from $x = 0$ to $x = 2$ m?

A) 16 J
B) 12 J
C) 0 J
D) 24 J

A) 16 J

$W = \int_0^2 \left(12 - 3x^2\right) dx = 24 - 8 = 16$ J. 24 J assumes the force stays at its initial 12 N over the whole 2 m.
Work Energy and Power › Work and Power
A turbine starts from rest with angular acceleration $\alpha(t) = 4t$ (rad/s², t in seconds). Through what angle does it turn in the first 3.0 s?

A) 18 rad
B) 27 rad
C) 36 rad
D) 54 rad

A) 18 rad

Integrate twice: $\omega = 2t^2$ and $\theta = \frac{2t^3}{3} = 18$ rad at $t = 3$ s. Treating $\alpha(3) = 12$ rad/s² as constant gives $\frac{1}{2}\left(12\right)\left(3\right)^2 = 54$ rad.
Torque and Rotational Dynamics › Rotational Kinematics
A thin-walled hollow sphere ( $I = \frac{2}{3}MR^2$ ⁠) rolls without slipping from rest down a ramp, dropping a vertical height h. What is its speed at the bottom?

A) $\sqrt{\frac{10gh}{7}}$
B) $\sqrt{2gh}$
C) $\sqrt{gh}$
D) $\sqrt{\frac{6gh}{5}}$

D) $\sqrt{\frac{6gh}{5}}$

$Mgh = \frac{1}{2}Mv^2\left(1 + \frac{2}{3}\right)$ ⁠, so $v = \sqrt{\frac{6gh}{5}}$ ⁠. $\sqrt{\frac{10gh}{7}}$ is the solid-sphere result, and $\sqrt{2gh}$ ignores rotational kinetic energy.
Energy and Momentum of Rotating Systems › Rotational Energy and Rolling
An oscillator's position is $x(t) = 0.10\cos\left(4t + \frac{\pi}{3}\right)$ (meters, seconds). What is its velocity at $t = 0$ ⁠?

A) −0.20 m/s
B) −0.40 m/s
C) −0.35 m/s
D) +0.35 m/s

C) −0.35 m/s

$v = \frac{dx}{dt} = -0.40\sin\left(4t + \frac{\pi}{3}\right)$ ⁠, which is $-0.40\cdot\frac{\sqrt{3}}{2} \approx -0.35$ m/s at $t = 0$ ⁠. −0.40 m/s would mean moving at the maximum speed, 0.40 m/s, which is reached only at equilibrium.
Oscillations

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Topic outline follows the College Board AP Physics C: Mechanics Course and Exam Description (2024 revised framework, Units 1–7); the AP name is used nominatively and no course or exam text is reproduced.
OpenStax University Physics Volume 1, consulted as a reference; no text copied.

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