Two trains `P` and `Q` are moving along parallel tracks same uniform speed of `20` m `s^(-1)`. The driver of train `P` decides to overtake train `Q` and accelerate his train by `1 ms^(-2)`, After `50 s`, train `P` crosses the engine of train `Q`. Find out what was the distance between the two trains initially. provided the length each is `400 m`.

Explanation

Let the initial distance between two trains be `x`.
Distance travelled by train `P` in `50 s`:
`S_(p)=ut+(1)/(2)at^(2)=20xx50+(1)/(2)xx1xx50^(2)=2250 m`
Distance travelled by train `Q` in `50` s:

`S_(Q)=ut =20 xx50=100 m`
Now `S_(P)-S_(Q) =2250-1000=1250 m`. This distance must be equal to the initial distance between the trains plus the sum of the length of the trains.
`x+800 =1250 rArr x=450 m`.