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 ?

Explanation

For train A, u = 72 km `h^(-1)=(72 times 1000)/(60 times 60)`
`=20ms^(-2), t=50s, a=0, s=s_(A)`,
As, `s=ut+1/2at^(2)`
`therefore s_(A)=20 times 50+1/2 times 0 times 50^(2)`
`" "=1000m`
For train B, u = 72 `kms^(-1)=20ms^(-2)`,
`a=1ms^(-2), t=50//S, S=s_(-B)`
As, `s=ut+1/2at^(2)`
`therefore S_(B)=20 times 50 +1/2 times 1 times 50^(2)`
`" "=2250m`
Taking the guard of the train B in the last compartment of the train B, it follows that original distance between two trains + length of train A + length of train `B=S_(B)-S_(A)`.
(Or) Original distance between the two trains
`=1250-800=450m`