While starting from a station, a train driver was instructed to stop his train after time T and to cover maximum possible distance in that time.
(a) If the maximum acceleration and retardation for the train are both equal to ‘a’, find the maximum distance it can cover.
(b) Will the train travel more distance if maximum acceleration is ‘a’ but the maximum retardation caused by the brakes is ‘2a’? Find this distance.

Answer

(a) `(1)/(4) aT^(2)` (b) Yes, `(1)/(3) aT^(2)`