distance/time problem

by michael makepeace
(Newcastle UK)

After the brakes are applied, the distance a train travels before coming to rest varies as the square of the speed of the train at the instant the brakes are applied. A train passing a signal box has to stop at a signal 1200 yards beyond the box. In order to do this when it is travelling at 60 m.p.h., the brakes must be applied when it is level with the box.

Calculate
(i) how far in front of the box the brakes must be applied when the train is travelling at 63 m.p.h,
(ii)how many seconds, to the nearest second, can elapse after passing the box, before the brakes have to be applied, when the train is travelling at 45 m.p.h.

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