# The time-average force of ball undergoing collision between walls

Why do we take the time between collisions e.g time of ball in air during collision between two walls to find time-average force like in the following question:

A “superball” of mass $m$ bounces back and forth with speed v between two parallel walls, as shown. The walls are initially separated by distance $l$. Gravity is neglected and the collisions are perfectly elastic. Find the time-average force $F$ on each wall.

Why do we take the time between collisions i.e time taken by the ball to cover $l$ distance find time-average force, when actually in momentum and impulse related question we are more concerned with time of collision which could be the time of interaction between the wall and the ball. But instead we choose to take time of the ball in air. Why do we do it?

$$F_{avg}\Delta t = \int {Fdt}$$