Impulse

When objects collide, they are only in contact for a brief instant, and the concept of force is not as relevant as that of impulse, which is the integral of the force over time. We can also define the impulse, to be the average force, _av, acting over a time interval, times the length of this interval, $\Delta$t. Newton's Second Law then tells us that the impulse equals the change in momentum. In other words, not only does the force matter but also how long it is applied. Impulse is very useful in the description of any force of very short duration like the impact of a tennis racket on a tennis ball.

= $\Delta$ = _f - _i = _av $\Delta$t

This relationship between average force, time interval, and impulse has important consequences:

• Assuming a given average force, increasing the contact time increases the impulse (example: follow-through in a tennis swing)
• Assuming a given momentum transfer, increasing the contact time decreases the average force (examples: air bags, active crash zones in cars)