Changes in Momentum and Force (Impulse) — AQA GCSE Physics (Higher / Separate)
A force acting on an object changes its momentum. Spreading the change over a longer time reduces the force.
Force and rate of change of momentum
A resultant force causes a change in momentum. The force equals the rate of change of momentum:
$$F = \frac{m , \Delta v}{\Delta t} = \frac{\Delta p}{\Delta t}$$
- F = force (N), Δp = change in momentum (kg m/s), Δt = time taken (s).
This is another form of Newton's second law.
Why a longer time reduces the force
For a given change in momentum, increasing the time over which the change happens decreases the force. This is the principle behind many safety features.
Safety applications
- Crumple zones in cars increase the collision time, reducing the force on the occupants.
- Air bags and seatbelts extend the stopping time.
- Cushioned/padded surfaces and gym mats increase the time of impact.
- A cricketer moving their hands back when catching a ball increases the time, reducing the force.
Worked idea
If the same change in momentum happens over twice the time, the average force is halved.
Exam tips
- Force = rate of change of momentum (F = Δp ÷ Δt).
- For a fixed momentum change, a longer time means a smaller force.
- Explain safety features (crumple zones, air bags, seatbelts) using this idea.
- Watch units: momentum in kg m/s, time in seconds.