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We will speak in terms of relative speeds and distances: the locomotive in front will be presumed stationary, and the train behind is approaching from a distance of 676km at 132kmh-1. This, if you like, is the situation as observed by the driver of the slower locomotive. The train must come to rest after 676km. If it decelerates steadily from 132kmh-1, then its average speed over this distance will be 66kmh-1. Thus the time taken to deceletrate is 676km/66kmh-1 = 10.242h The deceleration is therefore 132kmh-1/10.242h = 12.89kmh-2 (two decimal places) This is the minimum deceleration, because it ensures that the train stops gaining on the locomotive only at the last possible moment, when the two are adjacent. There are plenty of prefabricated equations for calculations of this kind, but sometimes it is better just to have a fiddle around.

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