Relating Impulse and Momentum
It turns out that there’s a direct connection between impulse and momentum. If you hit a pool ball with a cue, the cue imparts a certain impulse to the ball, causing the ball to end up with a particular momentum.
How can you relate impulse to momentum? Easy. The impulse you impart to an object gives it a change in momentum equal to that impulse, so
You might be confused about the units here. Impulse has MKS units of Ns, but momentum has MKS units of kgm/s. If the units are different, then how can these two be set equal to each other? Fortunately, the units are not actually different here. Recall that 1 N = 1 kgm/s^{2}. This means that 1 Ns = 1 kgm/s.
Sample question

If you hit a stationary 160.0g pool ball with a force of 100.0 N for 0.10 seconds, what is its final speed?
The correct answer is 62 m/s.

Use the equation

Find the impulse first:
Impulse = Ft = (100.0 N)(0.10 s) = 10 Ns

That impulse is the change in the pool ball’s momentum:

Now the pool ball’s initial momentum was zero, so the final momentum is:

Momentum equals mass times velocity, so to find speed (the magnitude of velocity), you can solve for v, like so:

Practice questions

You hit a hockey puck, mass 170 g, with a force of 150 N for 0.10 seconds. If it started at rest, what is its final speed?

You’re standing on an ice rink when another skater hits you, imparting a force of 200.0 N for 0.20 seconds. If you have a mass of 90.0 kg, what is your final speed?

You kick a 450g soccer ball with a force of 400.0 N for 0.20 seconds. What is its final speed?

You hit a 150g baseball with a force of 400.0 N for 0.10 seconds. The baseball was traveling toward you at 40 m/s. What is its final speed?
Following are answers to the practice questions:

88 m/s

Use the equation

Find the impulse:
Impulse = Ft = (150 N)(0.10 s) = 15 Ns

Because the initial momentum of the puck was zero, that impulse becomes the puck’s new momentum:
p = (150 N)(0.10 s) = 15 kgm/s

Momentum equals mass times velocity, so to find speed (the magnitude of velocity), you solve for v:


0.44 m/s

Use the equation

Find the impulse:
Impulse = Ft = (200.0 N)(0.20 s) = 40 Ns

Because your initial momentum was zero, that impulse becomes your new momentum:
p = (200.0 N)(0.20 s) = 40 kgm/s

Momentum equals mass times velocity, so to find speed (the magnitude of velocity), you solve for v:


178 m/s

Use the equation

2.Find the impulse:
Impulse = Ft = (400.0 N)(0.20 s) = 80 Ns

That impulse becomes the soccer ball’s new momentum:
p = (400.0 N)(0.20 s) = 80 kgm/s

Momentum equals mass times velocity, so to find speed (the magnitude of velocity), you solve for v:


227 m/s

Use the equation

Find the impulse first:
Impulse = Ft = (400.0 N)(0.10 s) = 40 Ns

That impulse becomes the ball’s change in momentum:

The baseball started with a momentum of (0.150 kg)(40 m/s) = 6 kgm/s (toward you), so its final momentum will be 40 kgm/s – 6 kgm/s = 34 kgm/s (away from you).

Momentum equals mass times velocity, so to find speed (the magnitude of velocity), you solve for v:
