Impulse
Change in momentum from a force over time.
Formula
Variables
Example
Airbags extend \Delta t to reduce force
How it works
Impulse measures how much a force changes an object’s momentum over a time interval. It works because a force acting for longer, or with greater size, produces a larger accumulated effect on motion, and that accumulated effect equals the change in momentum. This is why the same momentum change can come from a large force over a short time or a smaller force over a longer time.
When to use it
Use this formula when a force acts for a finite time and you want to find the resulting change in momentum, or vice versa. It is common in collisions, catching, batting, and any situation where forces act briefly and motion changes noticeably.
Worked example, step by step
A 0.15 kg tennis ball is struck by a racket with an average force of 300 N for 0.020 s. Use J = FΔt J = 300 × 0.020 J = 6.0 N·s Since J = Δp, the ball’s momentum changes by 6.0 kg·m/s. If the ball was initially at rest, its final momentum is 6.0 kg·m/s.
Common mistakes to avoid
- Using the final force at one instant instead of the average force over the contact time
- Forgetting that impulse and momentum change have the same numerical value and units (N·s = kg·m/s)
- Using mass directly in the formula without first connecting impulse to momentum change
Did You Know?
Airbags work by extending the time of impact, which lowers the force for the same change in momentum.
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