---
title: "AP Physics C: Mechanics Unit 3 Practice Test"
description: "A timed AP Physics C: Mechanics Unit 3 (Work, Energy, and Power) practice test in the AP format, drawn from 934 multiple-choice questions and 20 FRQs written for the unit. The standard version takes about 88 minutes."
canonical: "https://fiveable.me/ap-physics-c-mechanics/unit-test/3"
type: "unit-test"
subject: "AP Physics C: Mechanics"
unit: "Unit 3"
---

# AP Physics C: Mechanics Unit 3 Practice Test

## Overview

A timed AP Physics C: Mechanics Unit 3 (Work, Energy, and Power) practice test in the AP format, drawn from 934 multiple-choice questions and 20 FRQs written for the unit. The standard version takes about 88 minutes.

## Test Format

- 20 Multiple Choice Questions (40 minutes)
- 1 FRQ – FRQ 1 – Mathematical Routines (24 minutes)
- 1 FRQ – FRQ 2 – Translation Between Representations (24 minutes)

## Unit FRQs by Type

- [FRQ 1 – Mathematical Routines](/ap-physics-c-mechanics/frqs/mathematical-routines?unit=3): 6 questions
- [FRQ 2 – Translation Between Representations](/ap-physics-c-mechanics/frqs/translation-between-representations?unit=3): 3 questions
- [FRQ 3 – Experimental Design](/ap-physics-c-mechanics/frqs/experimental-design?unit=3): 6 questions
- [FRQ 4 – Qualitative/Quantitative Translation](/ap-physics-c-mechanics/frqs/qualitative-quantitative-translation?unit=3): 5 questions

## Practice Questions

### Question 1

A particle has mass $$m$$ and speed $$v$$. A second particle has mass $$3m$$ and speed $$2v$$. What is the ratio of the second particle's translational kinetic energy to the first particle's translational kinetic energy?

- (A) The ratio is $$6$$
- (B) The ratio is $$12$$
- (C) The ratio is $$18$$
- (D) The ratio is $$36$$

**Answer: (B)** Applying the formula $$K = \frac{1}{2}mv^2$$, the new energy is $$K' = \frac{1}{2}(3m)(2v)^2 = \frac{1}{2}(3m)(4v^2) = 12(\frac{1}{2}mv^2)$$, resulting in a ratio of $$12$$.

### Question 2

An object's momentum magnitude $$p$$ is doubled while its mass $$m$$ remains constant. By what factor does its translational kinetic energy change?

- (A) It increases by a factor of $$2$$
- (B) It increases by a factor of $$4$$
- (C) It increases by a factor of $$8$$
- (D) It increases by a factor of $$16$$

**Answer: (B)** Using the relationship $$K = \frac{p^2}{2m}$$, doubling the momentum ($$p \rightarrow 2p$$) results in $$K' = \frac{(2p)^2}{2m} = 4\frac{p^2}{2m}$$, which is a factor of $$4$$ increase.

### Question 3

A car starts from rest and accelerates with constant acceleration $$a$$. If the translational kinetic energy of the car is $$K_0$$ at time $$t_0$$, what is its translational kinetic energy at time $$2t_0$$?

- (A) The energy is $$K_0$$
- (B) The energy is $$2K_0$$
- (C) The energy is $$4K_0$$
- (D) The energy is $$8K_0$$

**Answer: (C)** For constant acceleration from rest, $$v = at$$, so velocity doubles when time doubles. Since $$K \propto v^2$$, doubling velocity quadruples the kinetic energy.

### Question 4

An engine delivers constant power $$P$$ to an object starting from rest. By what factor does the object's translational kinetic energy change if the time interval of acceleration is tripled?

- (A) It increases by a factor of $$3$$
- (B) It increases by a factor of $$9$$
- (C) It increases by a factor of $$27$$
- (D) It increases by a factor of $$81$$

**Answer: (A)** Since power is the rate of change of energy ($$P = \frac{dK}{dt}$$), constant power implies $$K = Pt$$. Therefore, tripling the time triples the kinetic energy.

### Question 5

An observer on the ground measures a car's kinetic energy as $$K$$. A second observer moves in the same direction as the car with half the car's ground speed. What value does the second observer measure for the car's kinetic energy?

- (A) The value is $$0.25K$$
- (B) The value is $$0.50K$$
- (C) The value is $$2.00K$$
- (D) The value is $$4.00K$$

**Answer: (A)** The relative speed is $$v_{rel} = v - 0.5v = 0.5v$$. Since $$K \propto v^2$$, the new energy is proportional to $$(0.5v)^2 = 0.25v^2$$, which is $$0.25$$ times the original energy.

### Question 6

A particle moves in a circle of radius $$R$$ with constant speed $$v$$. If the particle moves to a circle of radius $$2R$$ while maintaining the same centripetal force magnitude, what is the new translational kinetic energy?

- (A) It is half the original energy
- (B) It is the same as the original
- (C) It is twice the original energy
- (D) It is four times the original

**Answer: (C)** Centripetal force is $$F = \frac{mv^2}{R} = \frac{2K}{R}$$. If $$F$$ is constant and $$R$$ doubles, $$2K$$ must also double, meaning $$K$$ doubles.

### Question 7

The escape speed from a planet of mass $$M$$ and radius $$R$$ is $$v_{esc}$$. A second planet has mass $$2M$$ and radius $$2R$$. How does the translational kinetic energy of an object moving at the second planet's escape speed compare to one moving at the first planet's escape speed?

- (A) It is half the kinetic energy
- (B) It is the same kinetic energy
- (C) It is twice the kinetic energy
- (D) It is four times the energy

**Answer: (B)** Escape speed squared is proportional to $$M/R$$. For the second planet, $$v^2 \propto \frac{2M}{2R} = \frac{M}{R}$$. Since $$K \propto v^2$$, the kinetic energy is unchanged.

### Question 8

An object of mass $$m$$ starts from rest and is subjected to a net force $$F(t) = bt$$, where $$b$$ is a constant. How does the object's translational kinetic energy $$K$$ depend on the time $$t$$?

- (A) The energy $$K$$ is proportional to $$t$$
- (B) The energy $$K$$ is proportional to $$t^2$$
- (C) The energy $$K$$ is proportional to $$t^3$$
- (D) The energy $$K$$ is proportional to $$t^4$$

**Answer: (D)** Acceleration $$a \propto t$$, so velocity $$v = \int a dt \propto t^2$$. Kinetic energy $$K \propto v^2$$, so $$K \propto (t^2)^2 = t^4$$.

### Question 9

A cart of mass $$m$$ moving with speed $$v$$ collides with and sticks to an identical stationary cart. By what factor does the system's total translational kinetic energy change during the collision?

- (A) It decreases by a factor of $$4$$
- (B) It decreases by a factor of $$2$$
- (C) It remains exactly unchanged
- (D) It increases by a factor of $$2$$

**Answer: (B)** Conservation of momentum gives $$v_f = v/2$$. The final energy is $$K_f = \frac{1}{2}(2m)(v/2)^2 = \frac{1}{2}(2m)(v^2/4) = \frac{1}{2}(\frac{1}{2}mv^2)$$, which is half the initial energy.

### Question 10

A satellite orbits Earth in a circular path of radius $$r$$. If the satellite is moved to a circular orbit of radius $$2r$$, by what factor does its translational kinetic energy change?

- (A) It decreases by a factor of $$4$$
- (B) It decreases by a factor of $$2$$
- (C) It increases by a factor of $$2$$
- (D) It increases by a factor of $$4$$

**Answer: (B)** Orbital velocity squared is $$v^2 = GM/r$$. Thus, $$K \propto 1/r$$. Doubling the radius halves the kinetic energy.

## Review the Unit

- [3.1 Translational Kinetic Energy](/ap-physics-c-mechanics/unit-3/1-translational-kinetic-energy/study-guide/5nq7HC3BH3aW99nk)
- [3.2 Work](/ap-physics-c-mechanics/unit-3/2-work/study-guide/Y8X1HNf1OSe29MGP)
- [3.3 Potential Energy](/ap-physics-c-mechanics/unit-3/3-potential-energy/study-guide/I4y3a9MbuG2OgtXM)
- [3.4 Conservation of Energy](/ap-physics-c-mechanics/unit-3/4-conservation-of-energy/study-guide/wQp39tHxbOSvmKDT)
- [3.5 Power](/ap-physics-c-mechanics/unit-3/5-power/study-guide/aXNJ6Af1NIzpF1IM)

## Other Unit Tests

- [Unit 1: Kinematics](/ap-physics-c-mechanics/unit-test/1)
- [Unit 2: Force and Translational Dynamics](/ap-physics-c-mechanics/unit-test/2)
- [Unit 4: Linear Momentum](/ap-physics-c-mechanics/unit-test/4)
- [Unit 5: Torque and Rotational Dynamics](/ap-physics-c-mechanics/unit-test/5)
- [Unit 6: Energy and Momentum of Rotating Systems](/ap-physics-c-mechanics/unit-test/6)
- [Unit 7: Oscillations](/ap-physics-c-mechanics/unit-test/7)

## About This Document

Canonical Fiveable pages are available as Markdown at the same path plus `.md`.

- [llms.txt](https://fiveable.me/llms.txt): index of Fiveable's sections and URL patterns
- [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing
- [MCP server](https://fiveable.me/mcp): call Fiveable as tools instead of fetching pages (`https://fiveable.me/api/mcp`)
- [MCP server for AP teachers](https://fiveable.me/mcp/teachers): a teacher's classes, assignments and AP-rubric grading (`https://fiveable.me/api/mcp/teacher`)