Average velocity, speed and acceleration
You will be able to: Calculate interval averages without assuming constant motion.
What can endpoints tell you about a whole trip?
A cart moves 6 m right in 2 s, then 3 m left in 1 s. Over all 3 s, average velocity is +1 m/s while average speed is 3 m/s.
A useful starting point: Position, displacement and distance →
Words and symbols before equations
- Δt
- Elapsed time t_f − t_i, in seconds (s).
- Average velocity
- Displacement divided by elapsed time, in m/s.
- Average speed
- Distance divided by elapsed time, in m/s.
- Average acceleration
- Change in velocity divided by elapsed time, in m/s².
What this picture assumes
Fixed path: +6 m, then −3 m. This model compares interval averages only; it does not infer instantaneous velocities at the turnaround.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Displacement 3 m; distance 9 m; elapsed time 3 s. Average velocity 1 m/s; average speed 3 m/s.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Average velocity compresses an interval into one signed rate: +3 m/3 s = +1 m/s. It does not say the cart actually moved at +1 m/s at every instant. Average speed uses the 9 m path length and equals 3 m/s.
Average acceleration compares velocities, not positions. A velocity change from +6 to −2 m/s in 4 s gives −2 m/s². This could include slowing, a reversal and then increasing speed toward negative x.
An arithmetic mean of two speeds is generally not the trip average. Weight by time, or compute total distance and total time. Also, zero average acceleration only says the endpoint velocities agree; acceleration can vary between them.
A worked example, step by step
A cart travels +12 m in 3 s, then −4 m in 1 s. Find average velocity and average speed.
- Total time is 3 + 1 = 4 s.
- Displacement is 12 − 4 = 8 m; distance is 12 + 4 = 16 m.
- Average velocity = 8/4 = +2 m/s.
- Average speed = 16/4 = 4 m/s. They differ because the trip contains motion in both directions.
Do not divide by a final clock reading when the interval began after t = 0.
A car has the same velocity at two times. Must it have had zero acceleration between them?
Compare with an explanation
No. Its average acceleration is zero, but it could speed up and slow down between the endpoints.
Predict. Change one thing. Explain.
Keep both path legs fixed. Double only the total time and predict what happens to both averages.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Displacement 3 m; distance 9 m; elapsed time 3 s. Average velocity 1 m/s; average speed 3 m/s.
Fixed path: +6 m, then −3 m. This model compares interval averages only; it does not infer instantaneous velocities at the turnaround.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant position, velocity, acceleration or integral relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA particle travels 10 m east in 2 s and 4 m west in 2 s. Separately, its initial velocity is +5 m/s and final velocity is −2 m/s. Determine average velocity, speed and acceleration over the 4 s.
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Compare with the answer and four-point rubric
- 1 point: Displacement is +6 m, giving average velocity +1.5 m/s.
- 1 point: Distance is 14 m, giving average speed 3.5 m/s.
- 1 point: Δv = −7 m/s, giving average acceleration −1.75 m/s².
- 1 point: The acceleration result describes an interval average, not necessarily the acceleration at each instant.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Which average uses distance?
Average speed.
RECALL 2What are acceleration units?
m/s²: change in m/s per second.
RECALL 3When do average speed and |average velocity| agree in 1D?
When there is no direction reversal over the interval.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Average velocity, speed and acceleration
- v_avg = Δx/Δt; average speed = distance/Δt.
- a_avg = Δv/Δt.
- Averages alone do not determine the detailed motion.
Remember: Do not divide by a final clock reading when the interval began after t = 0.
Conditions: Fixed path: +6 m, then −3 m. This model compares interval averages only; it does not infer instantaneous velocities at the turnaround.
Refresh Kid · AP Physics C: Mechanics Unit 1 (official Unit 1) · Objectives 1.2.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 1.2, objectives 1.2.B. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. This is Mechanics Unit 1: Kinematics. Quantitative motion problems stay in one or two dimensions; the optional spatial view clarifies vector notation. Students should study calculus alongside this course. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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