When a force acts on an object that is moving, or able to move, a change in momentum occurs. Combining F = m a with a = (v - u) ÷ t gives the equation:
F = m Δv ÷ Δt
Here m Δv is the change in momentum and Δt is the time taken, so force equals the rate of change of momentum. Force is in newtons (N), change in momentum in kg m/s and time in seconds (s). Example: a 0.5 kg ball kicked from rest to 12 m/s has a change in momentum of 0.5 × 12 = 6 kg m/s. If the kick lasts 0.02 s, then F = 6 ÷ 0.02 = 300 N.
The same change in momentum can happen over a longer time, and then the force is smaller. A change in momentum of 60 kg m/s in 0.1 s needs a force of 600 N, but in 0.5 s it needs only 120 N.
Air bags, seat belts, gymnasium crash mats, cycle helmets and cushioned playground surfaces all work this way. They increase the time over which the person's momentum changes, so the force on the body is smaller and the risk of injury is reduced.