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An object , moving with a speed of 6.25...

An object , moving with a speed of ` 6.25 m//s `, is decelerated at a rate given by :
`(dv)/(dt) = - 2.5 sqrt (v)` where `v` is the instantaneous speed . The time taken by the object , to come to rest , would be :

A

2s

B

4s

C

8s

D

1s

Text Solution

Verified by Experts

The correct Answer is:
a
`(dv)/(dt)=-2.5sqrt(v)`
`int_(v=6.25)^(v=0)(dv)/sqrt(v)=int_(t=0)^(t)-2.5dt`
`[2v^(1//2)]_(2.25)^(0)=-2.5t`
`-2sqrt(6.25)=-2.5t`
`2(2.5)=2.5t rArr t=2 s`
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