When a driver of Shatabdi Express, running with velocity 108 km/hr, sights a goods train going ahead of him at a distance 50 m in the same direction on the same track, running with velocity 72 km/hr, he applies brakes. In order to avoid an accident, what should be the magnitude of the deceleration produced by the brakes?

Options

A. `5 ms ^(-2) `
B. `1 ms ^(-2)`
C. `3 ms ^(-2)`
D. None of these

Answer

B

Explanation

`v _(1) = (108 xx 1000)/(3600) = 30m//s, v _(2) = (72 xx 1000)/(3600) = 20 m//s.`
Initial velocity of Shatabdi Express
`v _(0) = v _(12) = v _(1) -v _(2) `
`v _(0) = 30 - 20 = 10 ms ^(-1)`
Now `v ^(2) =v _(0) ^(2) + 2ad`
Putting `v =0, v _(0) =10 ms ^(-1), d=50 m,`
`0= 100 + 2 xx a xx 50`
`therefore a xx 100 =- 100`
`therefore a =-1`
`therefore -a =1 ms ^(-2)`
`therefore` Deceleration `=1 ms ^(-2)`