# Impulse

In physics, the impulse of a force on an object is a vector quantity that measures how that force affects the object. It is equal to the average force that acts on an object in over a time period Δt multiplied by Δt.[1] It is often denoted using the letter J:



The impulse-momentum theorem states that the impulse that is applied to an object is equal to the object's change in momentum.

## Derivation

The impulse-momentum theorem can be derived using Newton's second law that relates force to the rate of change of momentum over time::



If the force has an average value Fave over a period of time Δt, we can rewrite this equation as:



Multiplying both sides by Δt, we recognise the left hand side as the impulse and the right as the change of momentum.

## Car Safety

An important application of impulse physics is car airbags. During a crash, the momentum of the car and its passengers will change and so they experience an impulse and therefore a force. If this force is too great, the passenger could be injured. This force depends on the size of the impulse delivered, but most importantly the length of time over which the impulse acts. By adding airbags into cars, the time over which the force acts, Δt, is increased which means, by Fave=J/Δt, that the force must be less. This reduces the chance of injury to passengers. Crumple zones in cars also work in a similar manner.