Newton's second law can be written in terms of momentum. The resultant force on an object is the rate of change of its momentum:
F = (mv − mu) ÷ t
Here F is the resultant force in newtons (N), m is the mass in kg, u is the initial velocity and v is the final velocity in m/s, and t is the time in seconds. The top of the fraction, mv − mu, is the change in momentum in kg m/s. Rearranged, change in momentum = F × t, so a resultant force of 10 N acting for 3 s changes the momentum by 30 kg m/s.
Worked example: a 1200 kg car travelling at 20 m/s is brought to rest in 4 s. Change in momentum = 0 − (1200 × 20) = −24 000 kg m/s. Force = −24 000 ÷ 4 = −6000 N. The size of the force is 6000 N and the minus sign shows it acts against the motion.
If the same change in momentum happens over a longer time, the force is smaller. Crumple zones, air bags and seat belts all make the collision last longer, so the force on the passengers is reduced.