Impulse⚠ unverified
Physics / Mechanics · Compute impulse delivered by a constant force
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| force | force | N | 1.0 | Force applied |
| time | time | s | 1.0 | Duration over which the force acts |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | J | N*s | Impulse, in newton-seconds (N*s), equal to the change in momentum |
The science & history
Understanding the Parameters
- $F$ — large force for short time can match a smaller force over longer time (same $J$).
- $\Delta t$ — contact duration in collisions is often milliseconds; average force is $J/\Delta t$.
- $J$ — same units as momentum; the “kick” applied to a free body.
Derivation (Approaching a Proof)
From $F = dp/dt$ (constant mass: $F = m a$), integrate over time:
$$J \equiv \int F\,dt = \Delta p.$$
For constant $F$, $J = F\,\Delta t$. This is why airbags increase $\Delta t$ to reduce peak $F$ for the same $\Delta p$.
History
Impulse–momentum is the integral form of Newton’s second law; standard in impact and ballistics analysis.
Related Concepts: Momentum, Newton's Second Law, Conservation Of Momentum, Work Constant Force
Notes: Registry calculator impulse (unverified). Constant (or average) force model.