Practice test

Kinematics Practice Test — 50 Questions

Use these three equations. Assume motion is in a straight line and use the signs given. Round to the nearest tenth when necessary.

\boxed{\text{Equation 1: }v_f=v_i+at}

\boxed{\text{Equation 2: }\Delta x=v_it+\frac12at^2}

\boxed{\text{Equation 3: }v_f^2=v_i^2+2a\Delta x}

Where v_f = final velocity, v_i = initial velocity, a = acceleration, t = time, and \Delta x = displacement.

Part A — Equation 1

1. A car starts at 5 m/s and accelerates at 3 m/s² for 4 s. What is its final velocity?

2. A runner is moving at 2 m/s and accelerates at 1.5 m/s² for 6 s. Find the final velocity.

3. A bicycle traveling at 12 m/s slows at −2 m/s² for 4 s. What is its final velocity?

4. A train starts from rest and accelerates at 2.5 m/s² for 8 s. Find its final velocity.

5. A skateboarder travels at 6 m/s and accelerates at 0.8 m/s² for 5 s. Find the final velocity.

6. A car traveling at 25 m/s brakes with an acceleration of −4 m/s² for 3 s. Find its final velocity.

7. A ball is moving at 8 m/s and experiences an acceleration of 2 m/s² for 7 s. Find its final velocity.

8. A motorcycle increases its velocity from 10 m/s to 30 m/s in 5 s. Find its acceleration.

9. A car increases its velocity from 4 m/s to 22 m/s with an acceleration of 3 m/s². How long does this take?

10. An object starts from rest and reaches 24 m/s after accelerating at 6 m/s². Find the time.

11. A cyclist moving at 18 m/s slows to 6 m/s in 4 s. Find the acceleration.

12. A train traveling at 30 m/s slows at −2.5 m/s² for 6 s. Find its final velocity.

13. A rocket sled begins at 15 m/s and accelerates at 7 m/s² for 3 s. Find its final velocity.

14. A cart moving at 9 m/s reaches 21 m/s after 4 s. Find its acceleration.

15. A car traveling at 20 m/s comes to rest in 5 s. Find its acceleration.

Part B — Equation 2

16. A car starts from rest and accelerates at 4 m/s² for 5 s. How far does it travel?

17. A runner begins at 3 m/s and accelerates at 2 m/s² for 4 s. Find the displacement.

18. A train starts at 10 m/s and accelerates at 1.5 m/s² for 6 s. Find its displacement.

19. A bicycle starts from rest and accelerates at 3 m/s² for 8 s. How far does it travel?

20. A car has an initial velocity of 5 m/s and accelerates at 2.5 m/s² for 4 s. Find its displacement.

21. A skateboarder moves initially at 4 m/s and accelerates at 1.2 m/s² for 5 s. Find the displacement.

22. A vehicle traveling at 20 m/s begins braking at −2 m/s². How far does it travel during the next 4 s?

23. A ball begins at 2 m/s and accelerates at 5 m/s² for 3 s. Find its displacement.

24. A cart starts from rest and accelerates at 1.8 m/s² for 10 s. Find its displacement.

25. A motorcycle starts at 12 m/s and accelerates at 3 m/s² for 5 s. Find its displacement.

26. A car starts from rest and travels 72 m in 6 s with constant acceleration. Find its acceleration.

27. An object starts from rest with an acceleration of 8 m/s² and travels 64 m. How long was it accelerating?

28. A runner begins at 5 m/s and accelerates at 1 m/s² for 7 s. Find the displacement.

29. A car initially travels at 15 m/s and accelerates at 2 m/s² for 3 s. Find its displacement.

30. A train traveling at 25 m/s slows at −3 m/s² for 5 s. How far does it travel during those 5 seconds?

Part C — Equation 3

No time variable here. Physics has mercifully removed one thing from your life.

31. A car starts from rest and accelerates at 4 m/s² over 50 m. Find its final velocity.

32. A runner moving at 3 m/s accelerates at 2 m/s² over 20 m. Find the final velocity.

33. A bicycle traveling at 5 m/s accelerates at 3 m/s² over 40 m. Find its final velocity.

34. A car traveling at 20 m/s brakes at −5 m/s² until it stops. Find its stopping distance.

35. A train traveling at 30 m/s slows at −3 m/s² until it stops. Find its stopping distance.

36. A motorcycle starts at 10 m/s and accelerates at 4 m/s² over 60 m. Find its final velocity.

37. A ball starts from rest and accelerates at 6 m/s² over 12 m. Find its final velocity.

38. A car increases its velocity from 10 m/s to 30 m/s over 100 m. Find its acceleration.

39. An object starts from rest and reaches 20 m/s while accelerating at 5 m/s². Find its displacement.

40. A skateboarder moving at 4 m/s accelerates at 2 m/s² across 30 m. Find the final velocity.

Part D — Mixed Problems

You choose the equation. No equation number is given because your teacher will presumably expect you to recognize them in the wild.

41. A car starts at 8 m/s and accelerates at 4 m/s² for 5 s. Find its final velocity.

42. A train starts from rest and accelerates at 3 m/s² for 7 s. Find its displacement.

43. A bicycle moving at 6 m/s accelerates at 2 m/s² across 25 m. Find its final velocity.

44. A car slows from 28 m/s to 12 m/s in 4 s. Find its acceleration.

45. A runner starts at 4 m/s and accelerates at 1.5 m/s² for 8 s. Find the displacement.

Part E — Formula Manipulation

Only five. Civilization survives.

46. Starting with

v_f=v_i+at

rearrange the equation to solve for a.

47. Starting with

v_f=v_i+at

rearrange the equation to solve for t.

48. Starting with

v_f^2=v_i^2+2a\Delta x

rearrange the equation to solve for a.

49. Starting with

v_f^2=v_i^2+2a\Delta x

rearrange the equation to solve for \Delta x.

50. Starting with

\Delta x=v_it+\frac12at^2

rearrange the equation to solve for a.

ANSWER KEY

Try not to wander down here until you’ve actually attempted them. Your future physics grade is watching.

1. 17 m/s

2. 11 m/s

3. 4 m/s

4. 20 m/s

5. 10 m/s

6. 13 m/s

7. 22 m/s

8. 4 m/s²

9. 6 s

10. 4 s

11. −3 m/s²

12. 15 m/s

13. 36 m/s

14. 3 m/s²

15. −4 m/s²

16. 50 m

17. 28 m

18. 87 m

19. 96 m

20. 40 m

21. 35 m

22. 64 m

23. 28.5 m

24. 90 m

25. 97.5 m

26. 4 m/s²

27. 4 s

28. 59.5 m

29. 54 m

30. 87.5 m

31. 20 m/s

32. 9.4 m/s

33. 16.3 m/s

34. 40 m

35. 150 m

36. 24.1 m/s

37. 12 m/s

38. 4 m/s²

39. 40 m

40. 11.7 m/s

41. 28 m/s

42. 73.5 m

43. 11.7 m/s

44. −4 m/s²

45. 80 m

46.
\boxed{a=\frac{v_f-v_i}{t}}

47.
\boxed{t=\frac{v_f-v_i}{a}}

48.
\boxed{a=\frac{v_f^2-v_i^2}{2\Delta x}}

49.
\boxed{\Delta x=\frac{v_f^2-v_i^2}{2a}}

50.
\boxed{a=\frac{2(\Delta x-v_it)}{t^2}}