AP Physics C: Mechanics Unit 3 Review: Work, Energy, and Power

Q: What's on the AP Physics Mech Unit 3 progress check (MCQ and FRQ)?

The AP Classroom Unit 3 progress check includes both MCQ and FRQ parts drawn from all five Unit 3 topics: Translational Kinetic Energy, Work, Potential Energy, Conservation of Energy, and Power. The MCQ section tests conceptual reasoning and calculation, while the FRQ part asks you to apply the work-energy theorem and conservation of energy to multi-part scenarios. Practice with matched questions at AP Physics C: Mechanics Unit 3 .

Q: How do I practice AP Physics Mech Unit 3 FRQs?

Unit 3 FRQs most often come from Conservation of Energy (3.4) and Work (3.2), asking you to set up energy equations, justify sign conventions, and interpret graphs of force vs. displacement. Practice by writing out full solutions that include a clear energy diagram, labeled variables, and a written justification, not just a numerical answer. Find Unit 3 FRQ practice at AP Physics C: Mechanics Unit 3 .

Q: Where can I find AP Physics Mech Unit 3 practice questions?

The best place to find AP Physics C: Mechanics Unit 3 practice questions, including multiple-choice and practice test sets, is AP Physics C: Mechanics Unit 3 . That page organizes MCQ and FRQ practice by topic, covering Translational Kinetic Energy, Work, Potential Energy, Conservation of Energy, and Power so you can target whichever topic needs the most work.

Q: How should I study AP Physics Mech Unit 3?

Start with Work (3.2) and the work-energy theorem before moving to Potential Energy (3.3) and Conservation of Energy (3.4), since those topics build directly on each other. Sketch energy diagrams for every problem, practice setting up integrals for variable forces, and check your sign conventions carefully. Finish by connecting Power (3.5) to the rate of energy transfer in real scenarios. Use the topic-by-topic resources at AP Physics C: Mechanics Unit 3 to track your progress.

15–25% of AP multiple choice
5 topics
AP exam review verified for 2027

Unit 3 builds the energy toolkit: kinetic energy, work as a line integral, potential energy stored by conservative forces, conservation of mechanical energy, and power as the rate of energy transfer. These ideas give you a second method for solving dynamics problems alongside Newton's second law from Unit 2.

Fiveable's AP Physics C: Mechanics Unit 3 review covers 5 topics, with guided practice questions for the unit.

start with 3.1 start unit practiceReview with a tutorFree, 24/7, real people, from UPchieve

AP Physics C: Mechanics unit 3 topics

3.1

Translational Kinetic Energy

Define K = (1/2)mv^2, recognize it as a scalar, and explain why its value depends on the observer's reference frame.

open guide

3.2

Work

Calculate work using W = Fd cos(theta) for constant forces and W = integral F dot dr for variable forces. Distinguish conservative from nonconservative forces and apply the work-energy theorem.

open guide

3.3

Potential Energy

Derive potential energy functions from conservative forces using delta U = -integral F dot dr, extract force from F_x = -dU/dx, and identify equilibrium from U(x) graphs.

open guide

3.4

Conservation of Energy

Apply E = K + U for conservative systems and W_nc = delta E when nonconservative forces act. Choose system boundaries to set up energy equations correctly.

open guide

3.5

Power

Calculate average power with P_avg = W / delta t and instantaneous power with P_inst = dW/dt or P = Fv cos(theta). Convert between watts and other energy-rate units.

open guide

Practice AP Physics C: Mechanics unit 3 questions

Try AP-style questions on unit 3, then use the review notes below for anything you miss.

Example AP-style MCQs

open all practice

MCQ

AP-style practice question

Question

An object falls through the air subject to a drag force $F_{drag} = -bv$ , where $b = 0.50$ kg/s. The object reaches a constant terminal speed of 20 m/s. What is the rate at which energy is dissipated by the drag force at this speed?

10 W, representing the magnitude of the drag force at the terminal speed.

100 W, representing the energy dissipated using half the velocity squared.

200 W, representing the rate of energy dissipation by the drag force.

400 W, representing the dissipation rate calculated with velocity squared.

answer in practice

MCQ

AP-style practice question

Question

A satellite moves in an elliptical orbit around Earth from perigee (closest point) to apogee (farthest point). System I is defined as the satellite only. System II is defined as the satellite and Earth. Which of the following correctly describes the change in total mechanical energy for each system during this motion?

System I remains constant; System II decreases

System I decreases; System II decreases

System I decreases; System II remains constant

System I remains constant; System II remains constant

answer in practice

Example FRQs

open all FRQs

FRQ

Block acceleration, friction, spring compression dynamics

1. A block of mass m = 2.0 kg is released from rest at the top of a frictionless ramp inclined at an angle θ = 30° above the horizontal, as shown in Figure 1. The block slides a distance d = 1.5 m along the ramp before reaching the bottom, where it then travels along a horizontal surface and compresses a spring with spring constant k = 800 N/m. The horizontal surface between the bottom of the ramp and the spring is rough, with a coefficient of kinetic friction μk = 0.25. The block travels a horizontal distance x = 0.60 m before making contact with the spring. After contacting the spring, the block compresses it a maximum distance s before momentarily coming to rest. The horizontal surface in contact with the spring is also rough with the same coefficient of kinetic friction μk = 0.25. Take g = 10 m/s².

Figure 1. Block sliding down a frictionless 30° ramp of length d = 1.5 m, then moving right on a rough horizontal surface (μk = 0.25) for x = 0.60 m before contacting a spring of constant k = 800 N/m attached to a fixed wall.

Describe the energy of the block-Earth system at the moment the block is released from rest at the top of the ramp and at the moment the block reaches the bottom of the ramp. Identify which forms of mechanical energy are present at each moment and explain how the total mechanical energy of the block-Earth system changes, if at all, as the block slides down the frictionless ramp.

ii.

Derive an expression for the speed $v_b$ of the block at the bottom of the frictionless ramp. Express your answer in terms of m, d, θ, g, and physical constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Derive an expression for the maximum compression distance s of the spring after the block contacts it. Express your answer in terms of m, d, θ, g, k, μk, x, and physical constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. After reaching the bottom of the ramp, the block slides along the rough horizontal surface a distance x = 0.60 m before contacting the spring.

Calculate the numerical value of the maximum compression distance s of the spring. Using the values m = 2.0 kg, d = 1.5 m, θ = 30°, g = 10 m/s², k = 800 N/m, μk = 0.25, and x = 0.60 m.

write this FRQ more Mathematical Routines FRQs in this unit

FRQ

Variable force, work-energy theorem, mass comparison

4. A block of mass m = 2.0 kg is initially at rest on a horizontal frictionless surface. A time-varying horizontal force F is applied to the block. The force varies with position x according to the equation F(x) = F₀(1 - x/d), where F₀ = 12 N and d = 3.0 m, as shown in Figure 1. The force is applied in the positive x-direction as the block moves from x = 0 to x = d.

Figure 1: Applied horizontal force F as a function of position x for F(x) = F₀(1 − x/d), with F₀ = 12 N and d = 3.0 m

The 2.0 kg block reaches a final speed v₁ at position x = d. The 4.0 kg block reaches a final speed v₂ at position x = d.

Indicate whether v₁ is greater than, less than, or equal to v₂ by writing one of the following.

v₁ > v₂
v₁ < v₂
v₁ = v₂

Justify your answer using qualitative reasoning beyond referencing equations.

Derive an expression for the speed v of the 2.0 kg block when it reaches position x = d. Express your answer in terms of m, F₀, d, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. The 2.0 kg block moves from x = 0 to x = d under the influence of the position-dependent force.

Indicate whether P₁ is greater than, less than, or equal to P₂. The average power delivered to the 2.0 kg block as it moves from x = 0 to x = 1.5 m is P₁. The average power delivered to the 2.0 kg block as it moves from x = 1.5 m to x = 3.0 m is P₂.

Briefly justify your answer.

write this FRQ more Qualitative/Quantitative FRQs in this unit

FRQ

Variable force work and kinetic energy

2. A block of mass $m = 2.0$ kg is initially at rest at position $x = 0$ on a frictionless horizontal surface, as shown in Figure 1. A horizontal force $F$ is applied to the block. The force varies with position according to $F(x) = F_0(1 - \frac{x}{d})$ , where $F_0 = 12$ N and $d = 3.0$ m, as illustrated in Figure 2. The force is applied until the block reaches position $x = d$ .

Figure 1. Block on a frictionless horizontal surface with position axis and applied force direction.

Figure 2. Applied force magnitude F as a function of position x for F(x) = F0(1 − x/d), with F0 = 12 N and d = 3.0 m.

Figure 3. Energy bar chart template for Scenario 1 at x = d, showing kinetic energy of the block and work done by the applied force.

An energy bar chart can be used to represent the kinetic energy $K_{block}$ of the block and the work $W_F$ done by the applied force F. On the energy bar chart in Figure 3, draw shaded bars to represent $K_{block}$ and $W_F$ when the block is at position $x = d$ .

The height of the shaded bars should be proportional to the relative values of $K_{block}$ and $W_F$ .
Any energy that is equal to zero should be represented by a distinct line on the zero-energy line.

Derive an expression for the speed $v$ of the block when it reaches position $x = d$ . Express your answer in terms of $m$ , $F_0$ , $d$ , and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. The block continues to move on the frictionless surface after the force stops being applied at $x = d$ .

Figure 4. Blank axes for sketching instantaneous power P versus position x from x = 0 to x = d.

On the axes in Figure 4, sketch a graph of the instantaneous power $P$ delivered by force $F$ as a function of position $x$ as the block moves from $x = 0$ to $x = d$ . The graph should clearly show: The instantaneous power $P$ delivered by the force $F$ to the block depends on both the force and the velocity of the block as it moves along the surface in Scenario 1.

The correct initial value at $x = 0$
The general shape of the curve
The correct final value at $x = d$

Describe one feature of the power graph from part (c) that would be different in Scenario 2 compared to Scenario 1, explicitly stating whether that feature increases or decreases. In Scenario 2, the block experiences a constant friction force of magnitude $f = 2.0$ N in addition to the variable force $F(x)$ . The block is again released from rest at $x = 0$ . A student claims that the speed of the block at $x = d$ in Scenario 2 will be less than the speed at $x = d$ in Scenario 1.

Justify your answer using physics principles.

write this FRQ more Representations FRQs in this unit

AP Physics C: Mechanics unit 3 practice test

A timed, AP-style test built only from unit 3 questions — multiple choice plus free response, scored with AI feedback. Use the standard format or build your own.

Take the unit 3 practice test

Unit 3 review notes

3.1

Translational Kinetic Energy

Translational kinetic energy is the energy an object has due to its translational motion. It is always a scalar and always non-negative. Because kinetic energy depends on v^2, doubling speed quadruples K. The value of K depends on the observer's reference frame, so two inertial observers can legitimately measure different values for the same object.

K = (1/2)mv^2: Kinetic energy in joules; m in kg, v in m/s. Scalar quantity, always greater than or equal to zero.
Scalar quantity: K has magnitude only, no direction. You add kinetic energies algebraically, not as vectors.
Frame dependence: Velocity is measured relative to an observer, so K changes with reference frame. There is no single 'correct' value of K for an object.
K vs v graph: A plot of K versus v is a parabola (quadratic). A plot of K versus m is linear at constant v.

A 2 kg object moves at 3 m/s in one frame and 5 m/s in another. Calculate K in each frame and confirm that both values are physically valid.

Quantity	Depends on mass?	Depends on speed?	Scalar or vector?
Kinetic energy K	Yes, linearly	Yes, quadratically	Scalar
Momentum p	Yes, linearly	Yes, linearly	Vector

3.2

Work

Work is the energy transferred into or out of a system by a force acting over a displacement. For a constant force, W = Fd cos(theta), where theta is the angle between force and displacement. For a variable force, W = integral from a to b of F(r) dot dr. The area under a graph of the force component parallel to displacement versus displacement equals the work done. Conservative forces do path-independent work; nonconservative forces like kinetic friction do path-dependent work.

W = integral F dot dr: General definition of work as a line integral. Reduces to Fd cos(theta) when the parallel force component is constant.
Conservative force: A force whose work depends only on initial and final positions, not the path taken. Examples: gravity, spring force. Work around a closed path is zero.
Nonconservative force: A force whose work is path-dependent. Kinetic friction and air resistance are the most common examples; they typically remove mechanical energy from the system.
Work-energy theorem: The net work done on an object equals its change in kinetic energy: W_net = delta K. This holds regardless of whether forces are conservative or not.
Sign of work: Positive work adds energy to the system; negative work removes it. Work is zero when force is perpendicular to displacement.

A spring with k = 200 N/m is compressed 0.10 m from equilibrium. Use the line integral to find the work done by the spring as it returns to equilibrium.

Force type	Path dependent?	Associated potential energy?	Example
Conservative	No	Yes	Gravity, spring
Nonconservative	Yes	No	Kinetic friction, air resistance

3.3

Potential Energy

Potential energy is stored energy associated with the configuration of a system whose objects interact through conservative forces. It is a scalar tied to position. The zero reference point is chosen by the analyst to simplify calculation; only changes in potential energy are physically meaningful. The key calculus relationship is delta U = -integral of F_cf dot dr, or equivalently F_x = -dU/dx in one dimension. A U(x) graph encodes both the potential energy and the force at every position.

delta U = -integral F_cf dot dr: Change in potential energy equals the negative of the work done by the conservative force. This is the defining relationship between conservative forces and potential energy.
F_x = -dU/dx: The conservative force in the x-direction equals the negative slope of the U(x) graph. Force points in the direction of decreasing potential energy.
Gravitational PE (near surface): U_g = mgy, where y is measured from the chosen zero reference. Valid when g is approximately constant.
Elastic PE: U_s = (1/2)k(delta x)^2 for a spring displaced delta x from its natural length.
Equilibrium from U(x): Equilibrium occurs where dU/dx = 0. A local minimum is stable equilibrium; a local maximum is unstable equilibrium.

Given U(x) = 3x^2 - 12x (in joules, x in meters), find the equilibrium position and determine whether it is stable or unstable.

System	Potential energy formula	Zero reference convention
Object near Earth's surface	U_g = mgy	Chosen height y = 0
Spring-mass system	U_s = (1/2)kx^2	Natural length x = 0
Two point masses (gravitation)	U = -Gm1m2/r	Zero at r = infinity

3.4

Conservation of Energy

Mechanical energy is E = K + U. When only conservative forces act within a chosen system and no work is done on the system from outside, E is constant: K_i + U_i = K_f + U_f. When nonconservative forces act, the work they do equals the change in total mechanical energy: W_nc = delta E = delta K + delta U. Choosing the system boundary carefully determines which forces are internal and which do work across the boundary.

E = K + U: Total mechanical energy is the sum of kinetic and potential energies. Conserved only when all internal forces are conservative and no external work is done.
W_nc = delta E: Work done by nonconservative forces equals the change in total mechanical energy. Friction typically makes delta E negative.
System selection: The choice of system boundary determines which energy transfers appear as work done on the system versus internal energy changes.
Energy dissipation: Nonconservative forces convert mechanical energy into thermal energy or sound. This energy is not lost from the universe but is no longer available as mechanical energy.

A 1 kg block slides down a 2 m ramp inclined at 30 degrees with a coefficient of kinetic friction of 0.2. Use energy methods to find the speed at the bottom.

Scenario	Mechanical energy conserved?	Equation to use
Only conservative forces	Yes	K_i + U_i = K_f + U_f
Friction or drag present	No	K_i + U_i + W_nc = K_f + U_f
External force does work	No	W_ext = delta K + delta U

3.5

Power

Power is the rate at which energy is transferred or converted. Average power is P_avg = delta E / delta t or equivalently W / delta t. Instantaneous power is P_inst = dW/dt. When a constant force acts on an object moving at velocity v, instantaneous power simplifies to P_inst = F_parallel * v = Fv cos(theta). The SI unit of power is the watt (1 W = 1 J/s).

P_avg = W / delta t: Average power equals total work divided by elapsed time. Units are watts (W) or joules per second.
P_inst = dW/dt: Instantaneous power is the time derivative of work. Use this when force or velocity varies with time.
P_inst = Fv cos(theta): For a constant force, instantaneous power equals the dot product of force and velocity. Only the component of force parallel to velocity contributes.
Watt: SI unit of power: 1 W = 1 J/s. Kilowatts (kW) are common in applied problems.

A motor exerts a constant 500 N force on a cart moving at 4 m/s at an angle of 30 degrees between force and velocity. Calculate the instantaneous power delivered.

Formula	When to use	Variables needed
P_avg = W / delta t	Total work over a time interval is known	W, delta t
P_avg = delta E / delta t	Energy change over a time interval is known	delta E, delta t
P_inst = dW/dt	Work is a function of time	W(t) expression
P_inst = Fv cos(theta)	Constant force, known velocity	F, v, theta

Key terms

Term	Definition
scalar	A physical quantity described by magnitude only, without direction. Both kinetic energy and work are scalars.

How to review unit 3

Topics students miss most

Miss rates come from Fiveable multiple-choice practice.

3.3

Potential Energy

46%747 tries

3.5

Power

44%349 tries

3.2

Work

35%567 tries

Common unit 3 mistakes

Treating work as a vector

Work is a scalar. The dot product F dot dr produces a signed number, not a vector. Students sometimes try to add work values as vectors, which gives wrong answers.

Forgetting the negative sign in F_x = -dU/dx

The conservative force equals the negative derivative of potential energy. Dropping the negative sign reverses the direction of the force and leads to incorrect equilibrium analysis.

Using conservation of mechanical energy when friction is present

K_i + U_i = K_f + U_f only holds when all forces doing work are conservative. If kinetic friction or drag acts, you must include W_nc = delta E or the answer will be too large.

Confusing average power with instantaneous power

P_avg = W / delta t gives the average rate over an interval. P_inst = Fv cos(theta) gives the rate at one instant. Using the average formula when instantaneous power is asked, or vice versa, produces incorrect results.

Setting the wrong zero for potential energy

The zero reference for U is a free choice, but it must stay consistent throughout a single problem. Switching the reference mid-calculation changes delta U and breaks the energy equation.

How this unit shows up on the AP exam

Deriving expressions using calculus

AP Physics C: Mechanics free-response questions frequently ask you to derive a symbolic expression for work, potential energy, or power using integration or differentiation. You should be comfortable setting up the line integral W = integral F dot dr for a given force function and applying F_x = -dU/dx to extract force from a potential energy expression.

Justifying energy conservation claims

Exam questions often ask you to explain whether mechanical energy is conserved in a given scenario and to justify your answer. You need to identify which forces act, classify them as conservative or nonconservative, and state how that classification determines whether E = K + U is constant or whether W_nc = delta E applies.

Interpreting graphs of energy and force

Questions may present a U(x) graph and ask you to identify equilibrium positions, determine the direction of force at a given point, or sketch the corresponding F(x) graph. You may also be asked to find work as the area under an F vs displacement curve or to read instantaneous power from a slope on an energy versus time graph.

More ways to review

Topic study guides

Open the individual guides for Unit 3 when you want a closer review of one topic.

browse guides

Practice questions

Use AP-style practice after you review the notes so you can check what you understand.

start practice

FRQ practice

Practice free-response reasoning and compare your answer with scoring guidance.

practice FRQs

Cram archive videos

Watch past review streams filtered to Unit 3 when you want a video walkthrough.

open videos

Official unit cheatsheet

Open the Fiveable one-page unit review, then explore visual cheatsheets for a quick refresher.

open unit cheatsheet

Score calculator

Estimate your broader AP score goal after you review the course and exam format.

open calculator

Unit 3 printables

Print the unit cheatsheets ($3) for Unit 3. Yours to keep, no subscription needed.

get printables

Frequently Asked Questions

What's on the AP Physics Mech Unit 3 progress check (MCQ and FRQ)?

The AP Classroom Unit 3 progress check includes both MCQ and FRQ parts drawn from all five Unit 3 topics: Translational Kinetic Energy, Work, Potential Energy, Conservation of Energy, and Power. The MCQ section tests conceptual reasoning and calculation, while the FRQ part asks you to apply the work-energy theorem and conservation of energy to multi-part scenarios. Practice with matched questions at AP Physics C: Mechanics Unit 3.

How do I practice AP Physics Mech Unit 3 FRQs?

Unit 3 FRQs most often come from Conservation of Energy (3.4) and Work (3.2), asking you to set up energy equations, justify sign conventions, and interpret graphs of force vs. displacement. Practice by writing out full solutions that include a clear energy diagram, labeled variables, and a written justification, not just a numerical answer. Find Unit 3 FRQ practice at AP Physics C: Mechanics Unit 3.

Where can I find AP Physics Mech Unit 3 practice questions?

The best place to find AP Physics C: Mechanics Unit 3 practice questions, including multiple-choice and practice test sets, is AP Physics C: Mechanics Unit 3. That page organizes MCQ and FRQ practice by topic, covering Translational Kinetic Energy, Work, Potential Energy, Conservation of Energy, and Power so you can target whichever topic needs the most work.

How should I study AP Physics Mech Unit 3?

Start with Work (3.2) and the work-energy theorem before moving to Potential Energy (3.3) and Conservation of Energy (3.4), since those topics build directly on each other. Sketch energy diagrams for every problem, practice setting up integrals for variable forces, and check your sign conventions carefully. Finish by connecting Power (3.5) to the rate of energy transfer in real scenarios. Use the topic-by-topic resources at AP Physics C: Mechanics Unit 3 to track your progress.

Ready to review Unit 3?Start with the notes, check the topic cards, and use the practice or resource links when they are available for this course.

start unit practice review topics

Unit 2Back

NextUnit 4Unit 4 – Linear Momentum