A lift moving in a mine pit of depth 4d meters begins to move vertically downwards from rest from point A, at time t = 0. First, it moves a distance d meters with constant acceleration g/2 m/s^2, and then it moves with the velocity attained at the end of that motion, for another distance of d meters. The lift then moves the remaining distance with constant deceleration so as to come to rest exactly at point B at a distance 4d meters below A. Find the total time taken by the lift to move down from A to B
