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Question

# Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 kmh−1 in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m/s2. If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them?

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Solution

## Step 1: Given that:Length of train A = Length of train B = 400m Initial velocity(uA) of train A = Initial speed of train B(uB) uA = uB = 72kmh−1 = 72×518ms−1=20ms−1 Train A is ahead of train B.Acceleration in train B(aB) = 1ms−2 Given time(t) = 50sec Step 2: Calculation of the original distance between train A and train B:The relative velocity of train B with respect to train A is given by;uBA=uB−uAuBA=20ms−1−20ms−1uBA=0Distance covered in the given time by train B with respect to A is given by the second equation of motion; s=ut+12at2 Let, sBA be the distance that is to be covered by train B to just cross train B.Putting the values, we get; sBA=uBA×t+12aBt2sBA=0×50sec+12×1ms−2×(50sec)2sBA=25×50sBA=1250m Here,The original distance between the train = The distance covered by train B with respect to train A to just cross train A(sBA) = 1250m Thus,The original distance between them is = 1250m.

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