A force acting over time changes momentum. The accumulated effect of that force is called impulse.

For a constant force acting during a time interval $\Delta t$,

$$\mathbf J=\mathbf F,\Delta t.$$

The impulse-momentum relation is

$$\mathbf J=\Delta\mathbf p.$$

Force-time graph

When force varies with time, impulse is represented by the signed area under the force-time graph. Positive and negative force contributions produce impulse in the corresponding directions.

The same momentum change can therefore be produced by a large force acting briefly or a smaller force acting for longer.

Example

A constant horizontal force of $20,\mathrm N$ acting for $0.5,\mathrm s$ produces impulse

$$J=20\cdot0.5=10,\mathrm{N,s}.$$

The object's momentum changes by

$$10,\mathrm{kg,m/s}$$

in the direction of the force.

Reducing forces by increasing time

For a fixed momentum change, increasing the stopping time reduces the average force. This is why padding, crumple zones and bending the knees when landing can reduce peak forces without eliminating the required momentum change.