All subjects · Mathematics · WME01 (M1)

Momentum and impulse

Momentum measures how hard a moving object is to stop. Impulse is what changes it. Both are vectors, so signs matter.

Definitions

These formulae are not in the booklet: learn them.

Signs

Choose a positive direction. A ball hitting a wall at 15 m/s and rebounding at 10 m/s has u = 15 and v = -10, so the change in velocity is 25, not 5.

Bouncing

For a ball dropped onto the floor, find the speed just before impact (free fall) and just after (from the rebound height), then impulse = m(v - u) with opposite signs.

Worked example

A 0.5 kg ball is dropped from 2.5 m and rebounds to 0.9 m. Find the impulse from the floor.

  1. Before: v2 = 2(9.8)(2.5) = 49, so 7 m/s down.
  2. After: u2 = 2(9.8)(0.9) = 17.64, so 4.2 m/s up.
  3. Up positive: I = 0.5(4.2 - (-7)) = 0.5 × 11.2.

Answer: 5.6 N s upwards

Key idea: Momentum = mv, impulse = mv - mu = Ft. Choose a positive direction: a rebound changes the sign of v.

Check yourself

  1. A 0.2 kg ball hits a wall at 15 m/s and rebounds along the same line at 10 m/s. Find the magnitude of the impulse.
    Show answer

    5 N s. 0.2(10 - (-15)) = 0.2 × 25 = 5 N s.

  2. A constant force of 6 N acts for 3 s on a 2 kg particle moving at 4 m/s in the direction of the force. Find its new speed.
    Show answer

    13 m/s. Ft = m(v - u): 18 = 2(v - 4), so v = 13 m/s.

  3. A 0.15 kg ball moving at 20 m/s is stopped by a catcher in 0.05 s. Find the average force.
    Show answer

    60 N. I = 0.15 × 20 = 3 N s. F = I/t = 3/0.05 = 60 N.

  4. A 0.4 kg ball falls from rest through 2.5 m, hits the floor, and rebounds at 4.2 m/s. Find the magnitude of the impulse from the floor, to 3 significant figures.
    Show answer

    4.48 N s. Impact speed 7 m/s. I = 0.4(4.2 + 7) = 4.48 N s.

  5. Find the momentum of a 1200 kg car moving at 15 m/s.
    Show answer

    18000 N s. mv = 1200 × 15 = 18000 N s.

  6. Which is a correct unit of impulse?
    • N/s
    • N s
    • J
    • N m
    Show answer

    N s. Impulse = force × time, so N s (equal to kg m/s).

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Sources

Last updated 7 November 2026. Spotted a mistake? Tell us.