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  • Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h^–1 in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m s^–2. If after

Q 3.7 Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h-1 in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m s-2. 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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Since both the objects are in motion it will be easier for us to do this problem in the relative frame. We take the train A as an observer.

Let the distance between the guard of B and driver of A be s.

Since both the trains are travelling with the same velocity initially, the relative initial velocity of B with respect to A(u) is 0.

Since A is not accelerating the relative acceleration would be the same as the acceleration wrt the ground frame, a= 1ms-2

The time taken to cover s distance by B wrt A = 50 s

Using the second equation of motion

\\s=ut+\frac{1}{2}at^{2}\\ s=\frac{1}{2}\times 1\times 50^{2}\\ s=1250\ m

The distance between the guard of A and driver of B initially is 1250 meter

 

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