Impulse Formula
Impulse (J) is the product of a force and the time it acts for: J = F × t. It is equal to the change in momentum an object experiences, so J = Δp = mv − mu. Its SI unit is the newton-second (N·s), which is the same as kg·m/s.
Impulse at a glance
| Quantity | Symbol / Formula | SI Unit |
|---|---|---|
| Impulse | J = F × t | N·s |
| Impulse–momentum theorem | J = Δp = mv − mu | kg·m/s |
| Force (constant) | F = Δp / t | N |
The impulse–momentum theorem
Newton's second law says force equals the rate of change of momentum: F = Δp / t. Rearranging gives F × t = Δp — that is, impulse equals the change in momentum. This is why a longer contact time reduces the force for the same change in momentum, the principle behind airbags, crumple zones and bending your knees when you land.
Because N·s and kg·m/s are the same unit, the two sides of J = Δp match dimensionally as well as numerically.
Worked examples
A 0.15 kg ball hits a wall at 20 m/s and bounces straight back at 20 m/s. Find the impulse.
- Take the initial direction as positive: u = +20 m/s, v = −20 m/s.
- Δp = m(v − u) = 0.15 × (−20 − 20)
- = 0.15 × (−40) = −6 kg·m/s.
- The impulse is 6 N·s, directed away from the wall (the sign shows direction).
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Frequently asked questions
Impulse J = F × t, and it equals the change in momentum, J = Δp = mv − mu.
The newton-second (N·s), which is equivalent to kg·m/s.
By the impulse–momentum theorem: the impulse on an object equals its change in momentum, J = Δp.