Why two colliding bodies exert varying forces on each other during the course of their collison? Suppose a bat hits a ball .What is the explanation of why the force is not constant during the course of the collison. At certain instants both ball and bat exert varying degrees of force on each other.What is its explantion? Could it be the motions of these two bodies that is a factor.And can we say that both ball and bat exert maximum force on each other when they are both at rest at that instant?

 A: Find the nearest box-spring mattress.  With your hand, execute a slow motion "impact" between your hand and the mattress.
You should notice that when your hand is not touching the mattress, there is, of course, no force between your hand and the mattress.
As your hand begins to touch the mattress, you should feel a very light force.  As your hand presses deeper into the mattress, the force on your hand should increase and increase.  At some point, based on the amount of speed your hand had at the beginning of this "simulation", your hand would come to a stop, then begin bouncing back upwards.  The force would decrease as your hand moves away from the mattress, until your hand is no longer in contact with the mattress, and the force is zero again.
Now, a bat is much, much harder than a mattress, but just like the mattress, its surface acts like a bunch of springs, in that the force increases the more it is compressed).  In the case of the bat and the ball, the springs have a much, much higher effective spring constant than the mattress (meaning the "springs" are stiffer, and the force increases much more sharply with compression), so their surfaces feel "hard".  Nonetheless, the surface of the bat and the ball compress slightly, leading to a smooth increase and decrease in the force as they collide and rebound, as your graph illustrates.
