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Two trains A and B of length 400 m each ...

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 ?

Text Solution

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We are given :
Speed of ech train `= 72 km h ^(-1) = 20 ms ^(-1)`
Acceleration of train `B = 1 ms ^(-2)`
Distance covered by train A in 50 second `S _(A) = 20 xx 50 = 1000 m.`
We are to calculate :
Distance covered by train B in 50 second
Using relation, `S _(B) = ut + (1)/(2) at ^(2) = (20 xx 50) + (1)/(2) xx 1 xx (50) ^(2) = 1000 + (1)/(2) xx 2500 = 2250 m`
Original distance between trains `= S _(B) - S _(A) = S = 2250 - 1000 = 1250 m.`
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