Impulse, J, is defined as follows:

J = FΔt

J = Impulse (N⋅s)
F = Force applied during a collision (N)
Δt = duration of a collision (s)

Impulse Momentum Theorem

Here’s the reason impulse is useful with momentum and collisions:

J = Δp
Impulse = Momentum Change

This statement is the Impulse Momentum Theorem.

It can also be written in this more practical way:

J = FΔt = Δp = mΔv

Or, just this:

FΔt = mΔv

Notice that impulse has the same units as momentum (kg⋅m/s):

Impulse units = (force unit)(time unit) = (N)(s) = (kg⋅m/s²)(s) = kg⋅m/s

Example 1:

A blue cart collides with a red cart for 0.40 seconds, applying an average force of 8.0 N.
a) What was the impulse in this collision?
Answer: J = FΔt = (8.0 N)(0.40 s) = 3.2 N⋅s = 3.2 kg⋅m/s

b) What is the change in the red cart’s momentum as a result of this collision?
Answer: Δp = 3.2 kg⋅m/s, because impulse equals momentum change.

Example 2:

A 2.0 kg red cart collides with a 6.0 kg blue cart. The red cart applies an average force of 10.0 N for an average of 0.50 seconds.
How much does the blue cart’s velocity change?

Answer:
FΔt = mΔv
(10.0 N)(0.50 s) = (6.0 kg)Δv
5.0 kg⋅m/s = (6.0 kg)Δv
Δv = 0.83 m/s

Bonus: The smaller red cart will have the same momentum change as the blue cart (5.0 kg⋅m/s), except in the opposite direction. Therefore, its velocity change is the following:

Δp = mΔv
5.0 kg⋅m/s  = (2.0 kg) Δv
Δv = 2.5 m/s