From the three examples on the last page, the same impulse can be applied through very different forces.
Braking gently applies a small force, while slamming on the brakes applies a large force; both bring the car to a complete stop, so both apply the same impulse.
How else are they different? Braking gently brings the car to a stop over a long time Δt, while slamming on the breaks does so over a short duration Δt. This leads to another way to express impulse: in terms of applied force and duration.
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Cushioning is an application of this definition of impulse as the product of force and time.
When a person jumps off a wall, his momentum changes rapidly—over a short Δt—which means that the applied force is large.
If he lands on a cushion, however, the same impulse is now delivered over a longer period of time, so he experiences a much smaller force. One hurts, while the other doesn't!
The same phenomenon is experienced when you bend your legs when landing.
Bending your knees extends the amount of time the impulse is applied, thereby reducing force you experience.
If you don't bend your knees, you can easily break your legs—even from a small height!
