When in physics class, we are generally shown a graph such as this:
And we are then told to calculate the impulse. We can easily do this by taking the integral of force with respect to time. But why is a force-time graph shaped like this? For example, if I threw a ball against a wall, why isn't the wall exerting just a constant force on the ball? Why does force vary over the time into the collision? And at what point in the collision does the local max occur?