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A body starting from rest, accelerates a...

A body starting from rest, accelerates at a constant rate a `m//s^2` for some time after which it decelerates at a constant rate b `m//s^2` to come to rest finally. If the total time elapsed is t sec, the maximum velocity attained by the body is given by

A

`(ab)/(a+b) tm//s`

B

`(ab)/(a-b) tm//s`

C

`(2ab)/(a+b) tm//s`

D

`(2ab)/(a-b) tm//s`

Text Solution

Verified by Experts

The correct Answer is:
A
Total time of motion = t
Duration of acceleration = t.
Duration of deceleration = t – t.
Given u = 0 , a = constant acceleration and b = constant deceleration.
`v = 0 + at.`
Also 0 =v -b (t-t.)`
` therefore v = at.`
From (ii) , -v = -bt + bt.
`rArr =at. = -bt+bt.`
`rArr (a+b)t. = bt rArr t. = (b)/((a+b) ) t`
But v = at.
Maximum velocity attained = at.
`rArr v = (ab)/((a+b)) tm//s`
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