A passenger train travelling at `30ms^(-1)` covers the railway platform of length 100 m in 6 seconds. Find the length of the train. If the train covers the two hills separated by a certain linear distance in 20 s then calculate the distance between the hills.

Explanation

Given, `v_(0)=30ms^(-1), t_(1)=6s, x=100m, t_(2)=20s`
Let L be the length of the train.
We know that for a uniform motion,
`s=v_(0)t`
Here `s=L+x`
`therefore" "L+x=v_(0)t`
`"or "L=v_(0)t_(1)-x`
`"i.e. "L=30xx6-100=180-100`
`L=80m`
Length of the train = 80 m.
Let y be the distance b/w the hills.
`L+y=v_(0)t_(2)`
`"i.e. "y=v_(0)t_(2)-L`
`"i.e. "y=30xx20-80=600-80=520 m`
Distance between the hills = 540 m.