When an object rebounds, its velocity changes direction. Choose a positive direction and give each velocity its sign before calculating final momentum minus initial momentum. The change in speed can be small even when the change in momentum is large.
The 2027 A-Level H2 Physics syllabus (9478) covers impulse and conservation of momentum in one-dimensional collisions. The original examples below show how to keep direction consistent and choose the system before writing an equation.
- Draw a positive-direction arrow before assigning signs.
- Find the ball’s momentum change with final minus initial.
- For conservation questions, define the system and check external impulse.
Worked example | A ball rebounds from a wall
A ball of mass 0.20 kg travels to the right at 6.0 m/s. It rebounds to the left at 4.0 m/s. Take right as positive. The initial velocity is +6.0 m/s and the final velocity is −4.0 m/s.
The initial momentum is +1.2 kg m/s and the final momentum is −0.80 kg m/s. The change is −0.80 − (+1.2) = −2.0 kg m/s. The net impulse on the ball is therefore 2.0 N s to the left.
If contact lasts 0.050 s and the wall supplies the net horizontal force during contact, the average horizontal force from the wall is −2.0 ÷ 0.050 = −40 N. The negative sign gives the direction. The size of the average force is 40 N.
When to use conservation of momentum
The ball alone receives an external impulse from the wall. Its momentum changes. For a two-cart system on a track, you can use conservation if the total external horizontal impulse during the collision is negligible.
For example, a 0.50 kg cart moving right at 4.0 m/s hits a stationary 1.0 kg cart. The first cart rebounds left at 1.0 m/s. With right positive, the initial total momentum is +2.0 kg m/s and the first cart’s final momentum is −0.50 kg m/s. The second cart must carry +2.5 kg m/s, so it moves right at 2.5 m/s.
As a check, the initial kinetic energy is 4.0 J and the final total is 3.375 J. Momentum conservation does not require the same total kinetic energy before and after this collision.
Reverse the positive direction to check your reasoning
In the ball example, choose left as positive. The initial velocity becomes −6.0 m/s and the final velocity becomes +4.0 m/s. The change is now +2.0 kg m/s. Positive means left under the new convention, so the physical result is the same.
Ask a study partner to give the direction in words after each signed result. If the sign changes after you reverse the axis but the words do not, you have kept the convention consistent.
Frequently asked questions
What if a question asks for magnitude only?
Report a positive magnitude. If it asks for direction too, use the sign convention or state the direction in words.
Can I use speed in the momentum calculation?
Use velocity with its sign in a one-dimensional calculation. Speed gives the magnitude only.
Official information
SEAB’s 2027 A-Level H2 Physics syllabus (9478), Mechanics, Section 6 Collisions. Checked 8 November 2026.