impulse

Impulse is the time-integral of force, and equals the change in momentum it produces. For a constant force F acting for a duration Δt, J = F·Δt. For variable forces, J = ∫F(t) dt. The SI unit is the newton-second, which is the same as kg·m/s — the unit of momentum, as it must be.

The insight is that it is the total impulse, not the peak force, that determines how much momentum a kick or push changes. Two collisions can deliver the same impulse with very different peak forces if one is long and the other short. Stretching the collision duration spreads the impulse over a longer interval and reduces the peak force proportionally. This is the principle behind airbags, crumple zones, foam helmet liners, parachutes, landing gear shock absorbers, and the boxer's slight pull-back on a punch to reduce peak force on a knuckle.

The opposite trick — concentrate the impulse into the shortest possible Δt — is used when peak force is what you want: a karate chop, a golf drive, the crack of a bullwhip, a hammer blow. Impulse is a fixed budget; how you spend it in time is the design decision.