Impulse
Impulse measures momentum transfer by a force acting over time. The same impulse can come from a large force briefly or a smaller force for longer.
How can different force histories cause the same momentum change?
Impulse depends on both force and time. On a force–time graph, impulse is the signed area under the curve.
For a changing force, impulse is the area under the force–time curve.
For the same momentum change, increasing the stopping time reduces the average force. Airbags, padding, and crumple zones exploit this relationship.
A wider low rectangle and a narrower tall rectangle can enclose the same signed area and produce the same Δp.
Impulse points with the force and can increase, decrease, or reverse an object's momentum.
The same impulse gives the same Δp, but a larger mass experiences a smaller change in velocity.