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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 kmh1 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 = 72kmh1 = 72×518ms1=20ms1

Train A is ahead of train B.

Acceleration in train B(aB) = 1ms2

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=uBuA

uBA=20ms120ms1

uBA=0

Distance 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+12aBt2

sBA=0×50sec+12×1ms2×(50sec)2

sBA=25×50

sBA=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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