IMPULSE
Impulse is force × time, and it equals the change in momentum: J = FΔt = Δp. Stretch the contact time and the force drops in step — the physics of every airbag.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
A 1-kilogram ball flying at 10 m/s has to be stopped. Whatever stops it — a wall, a glove, an airbag — delivers the same total push: force multiplied by time. That total is the impulse, and it has nowhere to hide.
The theorem
Impulse is force times time, J = FΔt, and it equals the change in momentum, Δp = mΔv. Bringing this ball to rest demands J = 10 N·s — a number fixed by the mass and the speed, no matter how the collision plays out.
The choice
Now the only freedom you have: how long. Grant the collision Δt = 50 ms and the average force is J/Δt = 200 N; the pulse rises and falls, peaking at twice that, 400 N. Halve the time and the force doubles; double it and the force halves.
Why we cushion
This is the whole reason for padding, crumple zones, and bending your knees when you land. Race a hard stop against a soft one: identical area under the curve — identical Δp — but the tall, narrow spike can shatter what the low, broad hill leaves untouched.
Audit
Audited: the area under the triangular F–t pulse integrates to the impulse to a part in ten-thousand; doubling the contact time exactly halves the force; and the impulse cancels the momentum precisely — v − J/m = 0, dead on zero.