In our test experiments on the air-track we just consider the case of
a stationary target (
) in various limits. The formulae simplify to
First the fascinating case where 
then we see that
ie there is complete transfer of linear momentum from one cart to the other.
From the formula we see that the stationary target will always gain velocity in the direction of the incoming cart. This is a very obvious result. However the incoming cart can end of moving in either direction depending on whether it is lighter or heavier than what it bumps into. (this is easily demonstrated as well)
Finally we consider the limiting cases where 
then the formulae give
the incoming cart is ``reflected'' back where it came from as if it had hit a brick wall
and the stationary
cart gain a very small velocity in the direction of the incoming cart as usual.
The other limit to consider is 
where
This case describes what happens when we hit a golf ball. The ball jumps off the
club at a velocity which is twice the velocity corresponding to the swinging
velocity of the club. The formula also accounts for the sling shot technique
used to bounce space ships deeper into space but this we will discuss later
when we reach the chapter on gravity.