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 :

Options

A. 1 s
B. 2 s
C. 4 s
D. 8 s

Answer

B

Explanation

`(dv)/(dt)=-5/2v^(1//2)`
`int_(25//4)^(v)v^(-1//2)dv=-5/2int_(0)^(t)dt`
`(|v^(1//2)|_(25//4)^(v))/(1/2)=-5/2|t|_(0)^(t)`
`v^(1//2)-sqrt(25/4)=-5/4t`
`sqrt(v)-5/2=-5/4t`
When `v=0impliest=2 s`