From Newton's Second Law and the definition of force:

(mv = final momentum, mu = initial momentum)

So, Ft = mv - mu

But, mv - mu = change in momentum

We call change in momentum impulse.

Impulse = Change in momentum = Ft

Units: Ns or Kgm/s

To achieve any particular change in momentum, you can either have a large force multiplied by a small time or a small force multiplied by a large time.

This explains how crumple zones work!

Volvo cars love collisions so much that they have crumple zones which make the collisions last longer. A longer time means that you can achieve the same change in momentum during a collision by applying a smaller force. And it is the force that hurts the passengers.

We can plot graphs of the force during a collision against time.

We can find the impulse, or change in the momentum, by calculating the area under the force-time graph.

Question:.

A car of mass 1000 kg is travelling at 40 m/s when it collides with a wall. The passenger can only survive when the maximum force on the car is 20 000 N.