Impulse and Vehicle Safety

Impulse — the product of a force and the time for which it acts:

impulse = FΔt

Impulse equals change of momentum — rearranging Newton's second law gives

FΔt = Δp = mv − mu

so impulse and change of momentum are the same quantity, measured in N s or kg m s⁻¹.

Area under a force–time graph — the impulse. For a varying force this is the only practical way to find it, and real collisions always involve a varying force.

Example: a force of 500 N acting for 0.080 s delivers an impulse of 40 N s, so the momentum changes by 40 kg m s⁻¹ whatever the mass involved.

The safety principle — in a collision, the change in momentum is fixed: the vehicle and its occupants must go from their initial velocity to rest. Since

F = Δp / Δt

and Δp cannot be changed, the only way to reduce the force is to increase the time over which the momentum change happens.

How each feature does this

Crumple zones — deform progressively, extending the time the car takes to stop rather than stopping it abruptly against a rigid structure.

Seat belts — stretch slightly and allow the occupant to move forward a short distance, extending their stopping time. They also prevent a second collision with the interior of the car.

Airbags — inflate and then deflate through vents as the occupant presses into them, spreading the impact over a longer time and over a larger area, which reduces the pressure as well as the force.

Crash helmets and playground surfaces — the same principle outside vehicles: a compressible layer extends the collision time.

Example: it is worth being precise about what these features do not do. None of them reduces the change in momentum, and none shortens the stopping distance of the vehicle before the crash. They act during the collision itself, trading a longer duration for a smaller force.