You made a stop at an intersection and then you are just about to drive across (just entering the intersection with a very slow speed) suddenly a car exactly the same as yours from the south is coming fast and collides into your car. After the collision, the two cars stick together and move towards a nearly north direction for a distance of 40 m before they stop. The kinetic frictional coefficient between the tires and the road is 1.0. Since the other car has the right of the way (there is no stop sign in the other direction but the speed limit is 25mph), so the accident seems to be your fault. But you feel very strongly that the other car was speeding. You go to court. The judge asked the following questions:
a) What kind of collision is this?
b) What is the total kinetic energy loss during the collision?
c) Provide the detailed mathematical evidence that proof the other car was speeding.