Impulse and the Concept of Impulsive Force

Many real forces -- a bat striking a cricket ball, a hammer striking a nail, one billiard ball colliding with another, an airbag decelerating a passenger -- act only for an extremely short interval of time, yet during that brief interval they can be extremely large. Such a very large force acting for a very short time is called an impulsive force. Because both the size of the force and the time for which it acts are difficult to measure separately and precisely in such cases, it is far more useful to describe the overall effect of an impulsive force using a single combined quantity, called impulse.

Impulse is defined as the product of force and the time interval for which it acts:

Starting from Newton's second law in its momentum form, $F = dp/dt$, and considering a (possibly large, possibly varying) force acting over a short interval from $t_1$ to $t_2$,

This is the impulse-momentum theorem: the impulse delivered to a body by a force, however large or however briefly it acts, is exactly equal to the resulting change in the body's momentum, $\Delta p$. When the force can be treated as effectively constant over the (short) interval $\Delta t$, this reduces to the simple working relation

which lets the average force exerted during an impact be calculated even when the exact way the force varies during the (very short) collision is not known -- a bat's exact push on a ball throughout the fraction of a second of contact is never known in detail, but the average force over that contact time can still be found this way, given only the ball's mass and its velocity just before and just after the hit. …