Two carts travel toward one another on a track. Each cart has a mass of 25kg. Cart 1 is moving at 20m/s[right] and Cart 2 is moving left at twice the speed. The carts collide in a head on collision cushioned by a spring with a spring constant 6.5x10^5 N/m. At the point of maximum compression of the spring, the carts both have the same velocity v(final).

a) What will be the velocity of each cart as the carts separate?

b) Determine the maximum compression of the spring?