Interesting Links (example problems):
During the collision of two objects, forces (which are equal but oppositely directed) act on the bodies. Those forces start out with zero values (just before the bodies touch), climb very rapidly to large values, and then fall off quickly to zero as the bodies separate (or as the energy is expended if they stick together).
The impulse of the collision is the average force times the time:
As Serway shows on page 239, the impulse is the change in the momentum of one body in the collision. That's different from the conservation of momentum principle, which describes the system (all colliding bodies). Think about it - it makes sense. When using a free body diagram to find a force, you have to cut around the body so that the force shows up in the free body. For a collision, if you want the force, you have to cut between the bodies so that the force appears in the free body!
The average force is not the initial value plus the final value, divided by two. Please look at Figure 9.4 on page 239. That method of computing an average would yield zero! If you think the average force is zero, try putting your hand between two railroad cars as they collide and couple! Instead, the average uses the Mean Value Theorem for Integrals from calculus - there is a rectangle whose area is the same as the area under the curve (see Fig. 9.4b). The height of that rectangle is the average force. The area under the curve is an integral. As equation 9.10 shows, that integral divided by the time interval yields the average force.
Figure 9.8 on page 242 graphs the forces on the two bodies in a collision. Since the forces are an action-reaction pair, they are opposite but equal. The blue curve represents the negative values.
The Impulse-Momentum Principle:
Impulse and momentum represents another way to evaluate dynamic situations. (The other twoways are using energy methods and Newton's Second Law.) It isn't (conceptually) any different from Newton's Second Law; in fact, as Serway shows, the two are equivalent. Because impulse equals the change in the momentum of a body, it's a vector. If you're careless with signs, or with vector notation, you'll get these problems wrong!
Example 1: Finding an average force
Example 2: The force on a bat