Impulse

Definition

The effect of a force applied over time — a big force for a short time can equal a small force for a long time.

$\vec{J} = \vec{F}\Delta t = \Delta \vec{p}$

Symbol: $\vec{J}$ · Unit: newton-second (N·s), equivalently kg·m/s

Technical definition

The integral of force over time, J = FΔt, equal to the change in momentum: J = Δp. This is the impulse–momentum theorem, a direct consequence of Newton's second law.

Example

Airbags stretch a crash's stopping time from about 0.01 s to about 0.2 s. The change in momentum is identical, but the longer time means a far smaller peak force on the driver — same impulse, survivable force.

Common confusion

Impulse is not just 'force'. A 10 N push for 5 seconds (50 N·s) changes momentum exactly as much as a 50 N shove for 1 second. Students who look only at force size miss the time factor — which is precisely why padding, crumple zones, and bending your knees when landing all work: they buy time, and time shrinks force.