AP Physics C: Mechanics Exam Instructions

The 200-word examination instruction list

AP Physics C: Mechanics asks you to translate a physical model into calculus and explain what the result means. Choose the system and sign convention before differentiating or integrating.

Start with the list or jump to exam requirements, worked examples, the Fencing Method or practice. The list combines task verbs with subject terms that help you interpret the question.

Essential instructions

No.	Instruction or term	Meaning or action
1	Identify	Name or pick out the item the question specifies.
2	State	Express the required point directly and clearly.
3	Describe	Report the relevant characteristics, events or pattern.
4	Explain	Connect the result to its cause, mechanism or reasoning.
5	Compare	Set the items side by side on the same relevant feature.
6	Interpret	Say what a statement, result or display means in context.
7	Justify	Give evidence for the claim and explain how that evidence supports, qualifies or defends it.
8	Evaluate	Weigh relevant evidence or criteria before reaching a judgment.
9	Determine	Work from the given information to establish an answer.
10	Calculate	Use numbers or other given information to work out a result.
11	Estimate	Find an approximate answer using the available clues.
12	Sketch	Show the required shape, relationships and labels.
13	Construct	Produce the specified representation using the information given.
14	Label	Attach the correct name to the indicated part.
15	Select	Choose only the number of options requested.
16	Check	Test the answer against the original instruction or condition.
17	Analyze	Break the information into relevant parts and explain how they relate.
18	Multiple-choice question	Select the answer that satisfies the full stem and any limiting words.
19	Free-response question	Produce your own answer and complete each labelled task.
20	Stimulus	Use the figure, extract or other material attached to the question.
21	Answer each subpart	Treat each lettered instruction as a separate job.
22	Hybrid digital	Check which questions are displayed digitally and which answers go in a paper booklet.

Subject terms and physical models

No.	Instruction or term	Meaning or action
23	Differentiate position	Find instantaneous velocity from the time derivative of position.
24	Differentiate velocity	Find instantaneous acceleration from the time derivative of velocity.
25	Integrate acceleration	Find velocity change from the signed time integral.
26	Integrate velocity	Find displacement from the signed time integral.
27	Integrate speed	Find total distance from the time integral of velocity magnitude.
28	Initial condition	Use the stated starting position or velocity to fix the integration constant.
29	Variable force	Write the force as a function of the relevant coordinate, speed or time.
30	Work integral	Integrate the component of force along the displacement path.
31	Potential from force	Integrate the negative of the conservative force component over position.
32	Force from potential	Take the negative spatial derivative of potential energy in one dimension.
33	Conservative force	Identify a force whose work between two points does not depend on the path.
34	Stable equilibrium	Identify a local minimum of potential energy in the one-dimensional model.
35	Unstable equilibrium	Identify a local maximum of potential energy in the one-dimensional model.
36	Turning point	Find where kinetic energy vanishes and the direction of motion reverses.
37	Instantaneous power	Use the dot product of force and velocity for the power delivered by that force.
38	Impulse integral	Integrate net force over the specified time interval.
39	Momentum derivative	Relate net external force to the time rate of change of momentum.
40	Centre-of-mass velocity	Divide total momentum by the system’s total mass.
41	Continuous mass distribution	Represent small mass elements using the density and appropriate length, area or volume element.
42	Linear mass density	Express mass per unit length and integrate when density varies.
43	Centre-of-mass integral	Integrate position times mass element and divide by total mass.
44	Moment-of-inertia integral	Integrate squared distance from the chosen axis over mass.
45	Parallel-axis theorem	Add mass times squared axis separation to the centre-of-mass moment of inertia.
46	Torque integral	Sum torques from distributed forces about a specified axis using an integral.
47	Angular impulse	Integrate net torque over time to find angular momentum change.
48	Angular momentum of a particle	Take the cross product of position relative to the origin and linear momentum.
49	Work by torque	Integrate torque about a fixed axis over angular displacement.
50	Rolling constraint	Relate translation and rotation for motion without slipping.
51	Static-friction direction	Determine which relative sliding would occur without friction and oppose that tendency.
52	Drag force	Model resistance as a function of speed with direction opposite relative motion through the medium.
53	Terminal speed	Find the speed where drag balances the other forces along the motion.
54	Differential equation of motion	Translate Newton’s law into an equation involving derivatives and solve or analyse it with initial conditions.
55	Sinusoidal solution	Match amplitude, angular frequency and phase to the equation and starting values.
56	Angular frequency	Use radians per unit time, equal to 2π divided by the period for periodic motion.
57	Small-angle approximation	Use sin θ approximately equal to θ in radians when the angle is small.
58	Simple pendulum period	Use the small-angle model and identify pendulum length and gravitational acceleration.
59	Effective spring constant	Relate the net restoring force to displacement near equilibrium.
60	Inverse-square gravitation	Find gravitational force from masses and inverse squared separation.
61	Gravitational potential energy	For two point masses use −GMm/r with zero chosen at infinite separation.
62	Circular-orbit speed	Set gravitational force equal to the required inward net force for a circular orbit.
63	Escape speed	Set the minimum energy for reaching infinity with zero remaining speed in the isolated model.
64	Orbital period	Relate the orbital circumference and speed for a circular orbit.
65	Dimensional check of an integral	Multiply the integrand’s units by the integration variable’s units.
66	Translate a graph into an integral	Identify the signed area and the physical quantity it represents.
67	Compare differential and integral forms	State whether the question asks for a local rate or a change over an interval.

Representations, experiments and calculations

No.	Instruction or term	Meaning or action
68	Choose a system	State which objects are included before applying a force, energy or momentum relationship.
69	Free-body diagram	Draw and label the forces acting on the specified object or system.
70	Net force	Find the vector sum of external forces on the selected system.
71	Resultant acceleration	Use the direction and magnitude of net force per unit mass.
72	Inertial reference frame	Use a frame in which a force-free object moves at constant velocity.
73	Displacement	Give the signed or vector change in position.
74	Velocity	Give the rate of position change with direction.
75	Speed	Give the magnitude of velocity.
76	Acceleration	Give the rate of velocity change with direction.
77	Constant acceleration	Use kinematics relationships only where acceleration is constant.
78	Position–time graph	Use the slope to find velocity at the requested time or interval.
79	Velocity–time graph	Use slope for acceleration and signed area for displacement.
80	Acceleration–time graph	Use signed area to find change in velocity.
81	Projectile motion	Treat horizontal and vertical components separately with a shared time.
82	Relative velocity	Find velocity with respect to the frame or object named in the question.
83	Weight	Use the gravitational force on the object, with direction toward the source.
84	Normal force	Draw the contact force perpendicular to the supporting surface.
85	Tension	Draw the pulling force along a taut cord or similar connector.
86	Static friction	Use the value needed to prevent sliding up to its maximum.
87	Kinetic friction	Draw friction opposite relative sliding at the contact.
88	Force pair	Identify equal and opposite interaction forces on different objects.
89	Translational equilibrium	Set the net force to zero for the system.
90	Uniform circular motion	Track changing velocity direction even though speed stays constant.
91	Centripetal acceleration	Find inward acceleration from speed squared divided by radius.
92	Radial direction	Resolve the quantity along the line from the centre of rotation.
93	Tangential direction	Resolve along the tangent perpendicular to the radial direction.
94	Work	Find energy transferred by a force acting through displacement.
95	Work–energy theorem	Relate total work on an object to its change in kinetic energy.
96	Kinetic energy	Use one-half mass times speed squared for translational motion.
97	Elastic potential energy	For an ideal spring, use one-half spring constant times displacement squared.
98	Mechanical energy	Add the kinetic and applicable potential energies of the system.
99	Energy transfer	Account for energy crossing the system boundary.
100	Conservation of energy	Account for energy within the system and transfers across its boundary.
101	Power	Find the rate at which energy is transferred or work is done.
102	Momentum	Multiply mass by velocity and keep track of direction.
103	Impulse	Use net force integrated over time, or the momentum change.
104	Force–time graph	Find impulse from the signed area under the net-force curve.
105	Conservation of momentum	Set initial and final total momentum equal when net external impulse is negligible.
106	Elastic collision	Use conservation of kinetic energy as well as the appropriate momentum condition.
107	Inelastic collision	Allow total kinetic energy to change while checking the momentum condition.
108	Perfectly inelastic collision	Assign a shared final velocity to objects that stick together.
109	Centre of mass	Locate the mass-weighted average position of the system.
110	Torque	Use the lever arm and force to find the turning effect about a chosen axis.
111	Lever arm	Find the perpendicular distance from the axis to the force’s line of action.
112	Angular displacement	Give the signed change in angle.
113	Angular velocity	Find the rate of change of angular position.
114	Angular acceleration	Find the rate of change of angular velocity.
115	Rotational inertia	Account for mass distribution relative to the specified rotation axis.
116	Rotational equilibrium	Set net torque about the chosen axis to zero.
117	Rotational kinetic energy	Use one-half rotational inertia times angular speed squared.
118	Angular momentum	For a rigid body rotating about a fixed axis, use rotational inertia times angular velocity.
119	External torque	Identify a turning effect produced by an interaction across the system boundary.
120	Rolling without slipping	Relate centre-of-mass speed to radius times angular speed.
121	Period	Find the time for one complete cycle.
122	Frequency	Find the number of cycles per unit time.
123	Amplitude	Find the greatest displacement from equilibrium.
124	Restoring force	Identify a force component directed back toward equilibrium.
125	Simple harmonic motion	Check that acceleration is proportional to displacement and opposite in direction.
126	Spring constant	Use the proportionality between force magnitude and displacement for an ideal spring.
127	Hydrostatic pressure	Use fluid density, gravitational field strength and depth to find the pressure increase.
128	Fluid at rest	Use the hydrostatic pressure relation and buoyancy instead of a flow model.
129	Vector component	Project the vector onto the named coordinate axis with the correct sign.
130	Sign convention	State which direction is positive and use it consistently.
131	Scale drawing	Use the requested scale when converting between arrow length and vector magnitude.
132	Ranking task	Order the listed cases and show equal rankings where warranted.
133	Translate a representation	Preserve the physical relationships when switching between words, equations, diagrams and graphs.
134	Linearise data	Choose transformed axes that yield a straight-line relationship for the proposed model.
135	Qualitative prediction	State how the outcome changes and give a physical reason.
136	Quantitative translation	Use the mathematical relationship to connect a numerical result with a qualitative claim.
137	Experimental design and analysis	Give a repeatable method, then explain how its measurements test the relationship.
138	Mathematical routine	Build the algebra from a relevant principle and show how it answers the prompt.
139	Hypothesis	State a testable prediction about a relationship.
140	Research question	Specify the focused question that the investigation will answer.
141	Independent variable	Identify what the investigator changes deliberately.
142	Dependent variable	Identify the measured outcome of the investigation.
143	Controlled variable	Identify a factor kept constant to help isolate the tested relationship.
144	Control group	Use the baseline comparison to interpret the treatment effect.
145	Experimental design	Use the stated groups, conditions and measurements to judge the experiment.
146	Sample size	Check how many observations, individuals or trials contribute to the result.
147	Representative sample	Check whether the selected cases reflect the population of interest.
148	Raw data	Use the measurements as originally collected.
149	Processed data	Use values calculated, combined or transformed from the original readings.
150	Outlier	Identify an observation unusually far from the general pattern.
151	Uncertainty	State or interpret the estimated doubt associated with a measurement or value.
152	Error bars	Read their meaning from the figure legend before interpreting them.
153	Repeatability	Consider agreement when the same method is repeated under the same conditions.
154	Reproducibility	Consider whether results agree when the method is repeated under changed conditions.
155	Validity	Consider whether the evidence or method answers the intended question.
156	Reliability	Consider whether a result or method gives consistent findings.
157	Confounding factor	Identify a factor that could contribute to the apparent relationship.
158	Operational definition	Use the measurable rule the study gives for the concept.
159	Correlation	Describe how variables vary together within the data.
160	Causation	Explain how one factor produces a change in another when evidence supports it.
161	Trend	The broad direction or pattern over a range.
162	Pattern	A regularity visible across observations or examples.
163	Scatterplot	Describe form, direction, strength and unusual points when relevant.
164	Line of best fit	Draw a line representing the overall pattern of plotted data.
165	Interpolate	Estimate within the range covered by the data.
166	Extrapolate	Estimate outside the observed range using an assumed pattern.
167	Read the axes	Identify the quantities, units and intervals on a graph before using a value.
168	Gradient from a graph	Calculate change in the vertical quantity per change in the horizontal quantity.
169	Area under a graph	Use the area only where the graph’s quantities make it the requested accumulated value.
170	Baseline measurement	Use the reading taken before the stated intervention or change.
171	Identify the reference group	Find the comparison used to isolate the change attributed to the intervention.
172	Explain a limitation	Identify the assumption or data issue that restricts the conclusion.
173	Keep the comparison fair	Compare quantities on the same stated basis and units.
174	Control treatment	Use the treatment intended to provide a reference comparison.
175	Residual	Subtract the predicted response from the observed response.
176	Significant figures	Give the requested number of meaningful digits.
177	Decimal places	Count the required digits to the right of the decimal point.
178	Dimensional analysis	Track units through the calculation to see whether the result has the requested dimension.
179	Order of magnitude	Estimate the relevant power-of-ten scale.
180	Calculate the percentage change	Divide the change by the starting value and multiply by 100.
181	Rate of change	Find the change in one quantity per unit change in another.
182	Unit rate	Calculate the amount corresponding to one unit of the other quantity.
183	Parameter	Use the fixed or adjustable quantity that defines a family of cases.
184	Model	Use a simplified mathematical or conceptual representation to address the task.
185	Table	Information arranged in rows and columns.
186	Graph	A visual display of data or a mathematical relationship.
187	Diagram	A drawing showing features, structure or relationships.
188	Scale	The intervals or measurement relationship used in a display.
189	Unit	The standard attached to a measurement, such as minutes or metres.
190	Unit conversion	Use a conversion factor to change the units while keeping the quantity the same.
191	Interpret the slope	Give the predicted change in response per one unit increase in the explanatory variable.
192	Interpret the intercept	Explain the predicted response at zero if zero makes sense in context.
193	Exact value	Leave the answer in a form that preserves its full value.
194	Give units	Attach the required measurement unit to the final result.
195	Find the exact value	Retain radicals, fractions, logarithms or π in exact form where appropriate.
196	Set up an equation	Translate the given conditions into a mathematical relationship.
197	Check the solution	Substitute the result into the original equation to verify it.
198	In terms of	Use the specified quantity or symbol in the final expression.
199	Solve	Find the values that satisfy the equation or inequality.
200	Substitute	Replace a variable with the given value or expression.

What the AP Physics C: Mechanics exam requires

College Board lists the regular 2027 exam for May 3. The exam is hybrid digital. Answer multiple-choice items in Bluebook and read the free-response prompts there. Handwrite the free responses in the supplied booklet.

Exam component	Format and weighting
I · Multiple choice	42 questions in 85 minutes, worth 50%. Expect standalone items and sets that use shared information.
II · Free response	4 questions in 95 minutes, worth 50%. Tasks cover mathematical routines, translation between representations, experimental design and analysis, and translation between qualitative and quantitative descriptions.
Calculator policy	Both sections allow approved four-function, scientific or graphing calculators. Bluebook provides scientific and graphing Desmos calculators.

Use the May 2027 timing when building a mock exam. In graph and experiment tasks, match the diagram or measurement plan to the particular relationship named in the prompt.

AP is a U.S.-based programme taken domestically and internationally. Confirm local reporting time and registration with your school or test centre. Practise with the official materials for your course and exam year.

Read the task before choosing a method

Write the governing principle before substituting. The derivative of position is a local rate, while the integral of velocity over time is a signed displacement. In rotational questions, identify the reference axis before writing a moment of inertia or torque.

Worked examples for common exam instructions

Differentiate to find acceleration

Prompt. For x(t) = 2t³ − 3t in SI units, find the acceleration at t = 2 s.

Answer. Velocity is 6t² − 3. Differentiating again gives acceleration 12t, so the acceleration is +24 m/s².

Integrate a variable force

Prompt. A force F(x) = 4x N acts in the positive x direction as an object moves from 0 to 3 m. Find the work.

Answer. Integrate 4x from 0 to 3. The result is 2x² evaluated at the bounds, or 18 J.

Determine a moment of inertia

Prompt. Set up and evaluate the moment of inertia of a uniform rod of mass M and length L about a perpendicular axis through one end.

Answer. Let x run from 0 to L and use dm = (M/L) dx. Integrating x² dm gives ML²/3.

Design and analyse a spring experiment

Prompt. Describe how to estimate a spring constant from periods measured with different attached masses.

Answer. Measure several oscillations for each mass, then calculate the period. Plot T² versus mass. In the ideal model the slope is 4π²/k, so k is 4π² divided by the fitted slope. Keep oscillations small and use the same spring.

Use the Fencing Method to build an answer

Start with a small, accurate response. Add the detail that fixes it to the question, then add the reason that connects them. Test the explanation on a new case.

Start. Speed increases.

Add context. The velocity and acceleration both point in the positive direction.

Add reasoning. Because the velocity and acceleration have the same sign, acceleration increases the magnitude of velocity.

Transfer. Reverse the velocity while keeping acceleration positive and reassess the speed.

Practise with the 200 terms

Choose one calculation, one graph task and one explanation. Mark where the response identifies the quantity or relationship, provides the requested representation and explains the result. Change one condition and try again.

Distinguish displacement from distance

Try it. Velocity is −2 m/s for 2 s and +3 m/s for 2 s. Find displacement and distance.

Check. Displacement is −4 + 6 = +2 m. Distance is 4 + 6 = 10 m.

Frequently asked questions

What should I show when a prompt says justify?

Give the relevant principle or evidence and connect it to the conclusion. For a direction or sign, state the convention that makes the direction or sign meaningful. Check the scoring guidelines for the specific released question.

Official sources and next reading

College Board AP Physics C: Mechanics exam information and released questions · AP calculator policy · 2027 AP exam schedule

Top 200 Vocabulary Word List for AP Physics C: Mechanics | Must Know Words for Common Examination Instructions