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Momentum and impulse practice

Momentum includes direction: p = mv. Impulse is the change in momentum and equals average net force multiplied by the time interval.

By ExamCat · Original study lesson · Published September 24, 2026

Understand the method

Choose an axis before subtracting momenta. In a collision, momentum of a system is conserved when its net external impulse is negligible over the interval. Kinetic energy need not be conserved in the same collision.

Worked example, step by step

A 0.20 kg ball moving at +10 m/s rebounds at −5 m/s. Find its impulse.

  1. Initial momentum is 0.20 × 10 = +2.0 kg·m/s.
  2. Final momentum is 0.20 × (−5) = −1.0 kg·m/s.
  3. Impulse is final minus initial: −1.0 − 2.0 = −3.0 N·s.
  4. If contact lasts 0.10 s, average net force is −3.0/0.10 = −30 N.

A mistake to watch for

Using only the difference in speeds misses the reversal. A rebound changes momentum more than stopping the same ball, because the final momentum points in the opposite direction.

Try it yourself: three questions

Write an answer before opening the explanation. For calculations, keep your units and intermediate steps; for concepts, state the reason for your choice.

1. A 2 kg cart moves at 3 m/s. Find momentum.

Show answer and explanation

6 kg·m/s in the direction of motion.

2. A constant net force of 8 N acts for 0.5 s. Find impulse.

Show answer and explanation

4 N·s along the force direction, equal to a momentum change of 4 kg·m/s.

3. A 1 kg cart at 4 m/s sticks to a stationary 3 kg cart. With negligible external impulse, find final velocity.

Show answer and explanation

Initial momentum is 4 kg·m/s and total mass is 4 kg, so final velocity is 1 m/s. Kinetic energy decreases even though momentum is conserved.

Build your next practice session

Mark the first step where your reasoning differed from the explanation. Turn that step into a question, answer it without looking, then change one condition in the example and explain what would change. A correct guess is a reason to revisit the method.

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Further reading

OpenStax Physics provides textbook background. The worked scenario and practice questions on this page were written independently for ExamCat.

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