Sled X is traveling along a straight track at 60m/s when its rocket engine shuts off and it immediately begins to decelerate at a constant rate of 5.0m/s2. At that same instant, Sled Y is 200m behind Sled X and begins to accelerate from rest along the same track with a constant acceleration of 3.0m/s2. Neglect friction and air resistance.
(a) Write algebraic expressions for the position of each sled as a function of time t measured from the instant Sled X starts to decelerate and Sled Y starts to accelerate.
(b) Determine whether Sled Y ever overtakes Sled X. Show quantitative reasoning to support your conclusion.
(c) Calculate the minimum separation distance between the two sleds and the time at which this minimum separation occurs.