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The brakes of a train which is travellin...

The brakes of a train which is travelling at `30 m//s` are applied as the train passes point A. The brakes produce a constant retardation of magnitude `3lambda m//s^(2)` until the speed of the train is reduced to `10 m//s`. The train travels at this speed for a distance and is then uniformly accelerated at `lambda m//s^(2)` until it again reaches a speed of `30 m//s` as it passes point B. the time taken by the train in travelling from A to B, a distance of 4 km, is 4 min. Sketch the speed time graph for this motion and calculate:-
(i) The value of `lambda` (ii) Distance travelled at `10 m//s`.

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