Impulse

When a very large force acts for a very short time (a bat striking a ball, a foot kicking a ball), it is called an impulsive force, and the physically useful quantity is its impulse — the accumulated effect of the force over that short time, obtained by integrating Newton's second law.

Starting from $F\,dt=dp$ (magnitude form) and integrating from initial time $t_i$ to final time $t_f$:

So impulse equals the change in momentum of the object. For a constant force, $J=F\Delta t=\Delta p$. Impulse is a vector, with SI unit newton-second (N s) — the same physical unit as momentum (kg m s$^{-1}$).

Average force. Even when the actual force varies during the short interval (e.g. the exact contact force during a kick), a useful average force can always be defined:

For a fixed impulse (fixed $\Delta p$), a smaller contact time $\Delta t$ produces a larger average force, and vice versa — the basis for several everyday safety illustrations:

• A cricketer catching a ball pulls the hands back with the ball's motion (increasing the effective stopping time $\Delta t$), reducing the average force on the hands, rather than stopping it abruptly.
• Airbags increase the time over which a passenger's momentum is brought to zero during a crash, reducing the average force experienced. …