A block is projected eastward along a straight, frictionless track inside a railroad car. The car moves east at constant speed vc. At t=0, the block has speed u relative to the car and immediately begins to decelerate uniformly at magnitude a (due to an internal braking mechanism) until it comes to rest relative to the car.
Derive an expression, in terms of vc, u, and a, for the block’s displacement relative to the ground during the time interval from t=0 until it stops relative to the car.