The Constant-Acceleration Equations · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Picking the right motion equation

Mathematics · Mechanics · ages 16-17
Name ______________________   Date ____________

  1. A sprinter goes from rest to 12 m/s in 4 s with constant acceleration. What distance in metres is covered?

    Answer: ______________

  2. A car starts at u = 4 m/s and accelerates at 3 m/s squared for 5 s. What is its final velocity in m/s?

    Answer: ______________

  3. A car starts at u equals 5 metres per second and accelerates at 2 metres per second squared for 4 seconds. What is its final velocity in metres per second?

    Answer: ______________

  4. A model gives t times (t minus 5) equals 0, so t is 0 or 5. What does t equals 0 mean?

    • The start of the motion
    • The object landing
    • A mistake in the algebra

  5. Starting from rest with acceleration 2 metres per second squared, an object reaches 36 m. Give the positive root for the time in seconds.

    Answer: ______________

  6. Starting from rest with acceleration 4 m/s squared, an object reaches 50 m. Give the positive root for the time in seconds.

    Answer: ______________

  7. You know u = 3 m/s, a = 2 m/s squared and t = 4 s, and you want s. Which single equation gives s directly?

    • s = (u + v)t / 2
    • v = u + at
    • v squared = u squared + 2as
    • s = ut + at squared / 2

  8. You know s is 20 m, u is 2 m/s, v is 8 m/s, and acceleration is unknown. Which equation finds t without a?

    • v equals u plus a t
    • v squared equals u squared plus 2 a s
    • s equals (u plus v) t over 2

  9. A ball thrown from a cliff reaches the ground below when t is 4 or negative 1. What does negative 1 mean?

    • The ball lands twice, at both times
    • The parabola sat at that height 1 second before the throw
    • The throw never happened

  10. A car starts at 5 metres per second and accelerates at 2 metres per second squared for 6 seconds. What distance in metres does it cover?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Picking the right motion equation W1-mt_Nyc3BcikQ9-s1

  1. 24 · s = (u + v)t over 2 = (0 + 12) times 4 over 2 = 24 m, the trapezium area.
  2. 19 · v = u + at = 4 + 3 times 5 = 19 m/s.
  3. 13 · v equals u plus a t: 5 plus 2 times 4 is 13.
  4. The start of the motion · t equals 0 marks the moment the clock starts, at the initial position.
  5. 6 · 36 equals t squared gives t is 6 or negative 6, and the journey takes 6.
  6. 5 · 50 = 2t squared gives t squared = 25, so t = 5 or t = negative 5, and the positive root fitting the journey is 5 s.
  7. s = ut + at squared / 2 · Only s = ut + at squared / 2 leaves out v, the letter you neither know nor want, giving s = 12 + 16 = 28 m.
  8. s equals (u plus v) t over 2 · Only s equals (u plus v) t over 2 avoids a entirely, giving t equals 4 seconds.
  9. The parabola sat at that height 1 second before the throw · The negative root belongs to the mathematics before t is 0, so the landing is at 4.
  10. 66 · s equals u t plus half a t squared: 30 plus 36 is 66.
Worksheet · LightMySky