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A train is at rest. It accelerates for a...

A train is at rest. It accelerates for a time ty at a uniform rate `alpha` and then comes to rest under a uniform retardation rate `beta` for time `t_(2)`. The ratio `t_(1)//t_(2)` is equal to

A

`(beta)/(alpha)`

B

`(alpha + beta)/(alpha)`

C

`(alpha + beta)/(beta)`

D

`alpha beta`

Text Solution

Verified by Experts

The correct Answer is:
A
Initial velocity = 0, v = u + at
Due to acceleration `alpha`, velocity is gained, `v = alpha t_(1)`
Due to retardation `beta`, velocity is lost in time `t_(2), v = beta t_(2)`
`therefore alpha t_(1) = beta t_(2)`
`therefore alpha t_(1) = beta t_(2)`
`therefore (t_(1))/(t_(2)) = (beta)/(alpha)`
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