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.

The learner question

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.

Core relationship
J=FΔt=ΔpJ = F\Delta t = \Delta p

For a changing force, impulse is the area under the force–time curve.

Force–time lab
force
time
impulse
10.0 N·s
final momentum
12.0 kg·m/s
final velocity
6.0 m/s
Force20 N
Duration0.5 s
Mass2.0 kg
Initial velocity1.0 m/s
Same impulse, different feel
Safety connection

For the same momentum change, increasing the stopping time reduces the average force. Airbags, padding, and crumple zones exploit this relationship.

Area is impulse

A wider low rectangle and a narrower tall rectangle can enclose the same signed area and produce the same Δp.

Sign matters

Impulse points with the force and can increase, decrease, or reverse an object's momentum.

Mass controls Δv

The same impulse gives the same Δp, but a larger mass experiences a smaller change in velocity.

Transfer check

Two stopping methods give the same change in momentum. Method B doubles the stopping time. What happens to the average force?