Motion Graphs: Gradients and Areas · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reading motion from graphs

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

  1. A velocity time graph is flat at 6 m/s for 5 s. What displacement in metres does that area represent?

    Answer: ______________

  2. A displacement time graph is a straight line from (0, 0) to (5, 20), with time in seconds and displacement in metres. What is the velocity in m/s?

    Answer: ______________

  3. A displacement time graph runs straight from (0, 0) to (5, 20). Time is in seconds and displacement is in metres. What is the velocity in metres per second?

    Answer: ______________

  4. A velocity time graph is flat at 6 metres per second for 5 seconds. What is the displacement in metres?

    Answer: ______________

  5. A velocity time graph is flat at 5 metres per second, then slopes straight down to zero. Which journey is that?

    • Waiting at rest, then speeding up steadily
    • Cruising at steady speed, then slowing steadily to a stop
    • Cruising, then turning back in one instant

  6. A velocity time graph is flat at 5 m/s and then slopes straight down to zero. Which journey is that?

    • Cruise at steady speed, then slow steadily to a stop
    • Wait at rest, then speed up steadily
    • Cruise, then instantly reverse direction
    • Speed up, then cruise at top speed

  7. Velocity rises steadily from 0 to 4 m/s over 10 s. What is the displacement in metres?

    Answer: ______________

  8. Velocity rises steadily from 0 to 4 metres per second over 10 seconds. What is the displacement in metres?

    Answer: ______________

  9. A velocity time graph shows a triangle of area 12 metres above the axis and a rectangle of area 8 metres below it. What is the displacement?

    • 4 m
    • 20 m
    • -4 m

  10. A velocity time graph shows a triangle of area 12 metres above the axis and a rectangle of area 8 metres below it. What is the total distance in metres?

    Answer: ______________

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Answer key

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

Reading motion from graphs W1-mt_KhJeCMYBSL-s1

  1. 30 · The area is a rectangle: 6 times 5 = 30 m of displacement.
  2. 4 · Velocity is the gradient: rise 20 over run 5 = 4 m/s.
  3. 4 · Gradient is rise over run: 20 divided by 5 is 4.
  4. 30 · The area is a rectangle: 6 times 5 is 30.
  5. Cruising at steady speed, then slowing steadily to a stop · Flat means constant velocity and a straight fall to zero means steady slowing to rest.
  6. Cruise at steady speed, then slow steadily to a stop · Flat means constant velocity and a straight fall to zero means steady deceleration to rest.
  7. 20 · The area is a triangle: half times 10 times 4 = 20 m.
  8. 20 · The area is a triangle: half times 10 times 4 is 20.
  9. 4 m · Displacement lets the lower area subtract: 12 minus 8 is 4.
  10. 20 · Distance adds every area as positive: 12 plus 8 is 20.
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