Unit 1 / Kinematics
Unit 1: 34 practice problems
Work from memory first. Draw a diagram, choose a system, and say why your model applies. The 30 selected questions revisit every topic in Kinematics; 4 additional problems at the end ask you to explain and apply the models. The worked solutions live on their own page.
This is mixed topic review: short concept checks, calculations, and experiment tasks appear together. Choose a topic below to revisit its lesson, then return to the questions that challenge your model.
Question 1 · AP topic 1.1
1. Topic 1.1 question 4
A robot starts at x = −2 m, moves to x = +5 m, then ends at x = +1 m. Find each displacement, the total displacement, and the distance.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 2 · AP topic 1.2
2. Topic 1.2 question 4
A tracker gives positions 0 m, 2 m, and 8 m at times 0 s, 1 s, and 3 s. Calculate average velocity during each interval and during the full 3 s.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 3 · AP topic 1.3
3. Topic 1.3 question 4
A cart’s velocity is +4 m/s for 2 s, then falls linearly to zero during the next 2 s. Sketch v versus t, and find displacement and the acceleration in each interval.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 4 · AP topic 1.4
4. Topic 1.4 question 4
A walkway moves +1.5 m/s. A traveler has +2.0 m/s relative to it. Find the traveler velocity relative to the building, then find the traveler velocity if they turn and walk at the same speed relative to the walkway.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 5 · AP topic 1.5
5. Topic 1.5 question 4
Resolve a 10 m/s launch at 37° using sin 37° ≈ 0.60 and cos 37° ≈ 0.80. Find the speed at the peak and the time to reach it using g = 10 m/s².
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 6 · AP topic 1.1
6. Topic 1.1 question 5
Draw two opposite displacement arrows, 4 m and 4 m, on a scale of 1 cm per meter. What can you conclude about the final position? What cannot you conclude about the travel time?
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 7 · AP topic 1.2
7. Topic 1.2 question 5
A cart moving right has positive acceleration. Describe what happens to its speed. Then repeat for a cart moving left with the same positive acceleration.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 8 · AP topic 1.3
8. Topic 1.3 question 5
Derive Δx = ½(v_i + v_f)Δt from a straight velocity–time graph. State the condition needed for that graph.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 9 · AP topic 1.4
9. Topic 1.4 question 5
A ground velocity graph rises from 4 to 10 m/s in 3 s. Sketch the velocity graph measured from a frame moving +2 m/s. Compare slopes and accelerations.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 10 · AP topic 1.5
10. Topic 1.5 question 5
Draw x–time, y–time, vₓ–time, and vᵧ–time graphs for a horizontal launch. Describe one feature that connects each position graph to its velocity graph.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 11 · AP topic 1.1
11. Topic 1.1 question 6
A student says “negative acceleration always means slowing down.” Explain why a direction sign by itself cannot establish that claim.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 12 · AP topic 1.2
12. Topic 1.2 question 6
Two position–time curves share the same endpoints. One is a straight line; the other bends upward. Explain how their full-interval average velocities can match while their instantaneous velocities differ.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 13 · AP topic 1.3
13. Topic 1.3 question 6
A falling ball experiences increasing air resistance. Sketch the qualitative velocity and acceleration graphs with downward positive. Explain why a constant downward acceleration graph would fail.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 14 · AP topic 1.4
14. Topic 1.4 question 6
Cars A and B have x_A = 2 + 4t and x_B = 14 + 2t, with x in meters and t in seconds. Use relative motion to find when they meet.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 15 · AP topic 1.5
15. Topic 1.5 question 6
Derive how horizontal range depends on table height h for fixed horizontal launch speed u. Which axes would linearize experimental range data?
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 16 · AP topic 1.1
16. Topic 1.1 question 1
A person walks 7 m east, then 3 m west. With east positive, which pair is correct?
- Distance 10 m; displacement +4 m
- Distance 4 m; displacement +10 m
- Distance 10 m; displacement −4 m
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 17 · AP topic 1.2
17. Topic 1.2 question 1
A runner returns to the start after 20 s. Which statement must be true?
- Average velocity is zero
- Average speed is zero
- Instantaneous velocity was always zero
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 18 · AP topic 1.3
18. Topic 1.3 question 1
A velocity–time graph lies below zero and slopes upward. What does it describe?
- Moving negative and initially slowing down
- Moving positive and speeding up
- No motion because velocity is negative
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 19 · AP topic 1.4
19. Topic 1.4 question 1
A bus moves +10 m/s relative to the road. A rider walks −1 m/s relative to the bus. What is the road velocity?
- +9 m/s
- −11 m/s
- +11 m/s
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 20 · AP topic 1.5
20. Topic 1.5 question 1
A horizontally launched ball has negligible air resistance. Which quantity stays constant during flight?
- Horizontal velocity
- Vertical velocity
- Speed
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 21 · AP topic 1.1
21. Topic 1.1 question 2
A velocity component is −5 m/s. What is the speed?
- −5 m/s
- 5 m/s
- It cannot be found without acceleration
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 22 · AP topic 1.2
22. Topic 1.2 question 2
Velocity changes from −3 m/s to −7 m/s in 2 s. What is the average acceleration?
- +2 m/s²
- −2 m/s²
- −5 m/s²
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 23 · AP topic 1.3
23. Topic 1.3 question 2
What does the area under an acceleration–time graph give?
- Position
- Velocity change
- Acceleration change
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 24 · AP topic 1.4
24. Topic 1.4 question 2
Two inertial observers move at constant velocity relative to each other. Which measurement must agree?
- Object velocity
- Object position
- Object acceleration
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 25 · AP topic 1.5
25. Topic 1.5 question 2
A projectile is at the highest point of an angled flight. Which statement is correct?
- Its total velocity is necessarily zero
- Its vertical velocity is zero and acceleration is downward
- Gravity is briefly zero
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 26 · AP topic 1.1
26. Topic 1.1 question 3
You reverse the positive direction of an axis. What happens to a nonzero displacement component?
- Its sign reverses; its magnitude stays the same
- Its magnitude doubles
- Both its sign and physical direction reverse
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 27 · AP topic 1.2
27. Topic 1.2 question 3
A car travels around a circular bend at fixed speed. Is it accelerating?
- No; only changing speed causes acceleration
- Yes; the velocity direction changes
- Only if its position is negative
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 28 · AP topic 1.3
28. Topic 1.3 question 3
At the highest point of a vertical toss without air resistance, which statement is correct?
- Velocity and acceleration are both zero
- Velocity is zero; acceleration is downward
- Acceleration changes from upward to downward
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 29 · AP topic 1.4
29. Topic 1.4 question 3
A car has road velocity +6 m/s and a truck +10 m/s. What is the car velocity relative to the truck?
- +4 m/s
- −4 m/s
- +16 m/s
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Question 30 · AP topic 1.5
30. Topic 1.5 question 3
Horizontal launch speed doubles at fixed table height. How do fall time and range change?
- Time doubles; range quadruples
- Time is unchanged; range doubles
- Both double
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
See this question in its original context ↗Review the model ↗Separate worked solution ↗
Explain and apply the model
Try these problems before opening the solutions. State your assumptions, show the diagram or calculation, and explain what makes your answer follow.
Audit a robot’s motion report
A robot starts at x = −3 m, goes to x = +5 m, and returns to x = +1 m in a total of 6 s. East is positive and x = 0 is a doorway. At the final instant its velocity is 2 m/s west and its acceleration is 0.50 m/s² east.
(a) Calculate final position, total displacement, distance, average velocity, average speed, final speed, and final signed acceleration. Classify each of these measurements as scalar or vector; your classification must explicitly include position, displacement, distance, velocity, speed, and acceleration.
(b) Write symbols for position, displacement, velocity, and acceleration with an arrow above each symbol. Write the constant-acceleration vector equation for velocity using that notation and its separate x-component equation. Explain what the arrow and the signed component each communicate; use the robot’s final velocity as an example.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
Worked solution and rubric →Revisit the worked example →Read the relevant section →
Choose a point model and resolve a moment
A 0.80 kg charged cart crosses a 12 m straight track; its total charge is known. The motion question concerns only translational position. A position record gives x = 4.00, 4.41, 6.25, and 9.00 m at t = 2.00, 2.10, 2.50, and 3.00 s. A separate cart’s velocity record gives v = 6.00, 6.61, 9.25, and 13.00 m/s at those same times. Treat the records as smooth and sufficiently precise; no variable-acceleration equation is needed.
(a) Explain when the first cart can be treated as a single point object. Explicitly state what happens to its size, shape, and internal configuration, and whether its mass and total charge remain in the model. Give a question for which this object model would be inadequate.
(b) From the position record, calculate average velocities over 2.00–3.00 s, 2.00–2.50 s, and 2.00–2.10 s. Use the shrinking intervals to estimate the instantaneous velocity at 2.00 s. Explain why the shortest average is more local and why its precision cannot be guaranteed merely by making the interval shorter.
(c) Repeat the shrinking-interval calculation with the separate velocity record to estimate instantaneous acceleration at 2.00 s. Combine this with your numerical sequence in part b to report both instantaneous velocity and instantaneous acceleration estimates. Compare their units and numerator quantities, and explain how each very small interval average approximates its instantaneous value.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
Worked solution and rubric →Revisit the worked example →Read the relevant section →
Derive and cross-check a braking model
A cart begins at x₀ = −5 m with vₓ₀ = +12 m/s. During the next 3 s its acceleration is constant at aₓ = −3 m/s². Use a single right-positive axis.
(a) Derive all three constant-acceleration equations vₓ = vₓ₀ + aₓt, x = x₀ + vₓ₀t + ½aₓt², and vₓ² = vₓ₀² + 2aₓ(x − x₀) from the slope and signed area of a velocity–time graph. Show the time elimination for the third equation and state the condition shared by the three equations.
(b) Calculate the final signed velocity and position after 3 s with the first two equations. Independently check the final velocity’s square using the third equation. Explain why taking only a square root would not fix the direction of the final velocity.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
Worked solution and rubric →Revisit the worked example →Read the relevant section →
Specify two observers’ frames
A bus rear passes a lamp post while traveling east at a constant 9 m/s. A road observer stands at the lamp post and another observer sits at the bus rear. Three seconds after that passing event a cyclist has road coordinate +33 m and road velocity +6 m/s. All motion is along the straight east–west road.
(a) Describe the reference frame of each observer. Specify an origin attached to the observer, an axis and positive direction, a clock zero event and units. Explain why the two frames can be regarded as inertial for this comparison.
(b) Using your stated frames, calculate the cyclist’s position and signed velocity relative to the bus at 3 s. Explain how the cyclist can be east of the bus rear while moving west relative to it.
Your written working
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. The problem remains available above; keep your work on paper or in your own notes.
Written working stays in this browser.
Worked solution and rubric →Revisit the worked example →Read the relevant section →