Rate of decrease of velocity of an object moving with `6.25m//s is (dv)/(dr) =-2.5 sqrtv.` Where v is instantaneous speed. Time taken by object to come to rest is .............

Options

A. 1s
B. 2s
C. 4s
D. 7s

Answer

B

Explanation

`(dv)/(dt)=- 2.5 sqrtv`
`therefore (dv)/(sqrtv)=-2.5 dt`
`therefore int _(6.25 ) ^(0) (dv)/(sqrtv) =-2.5 int _(0) ^(t) dt`
`therefore [-2 sqrtv]_(6.25) ^(0)=-2.5t`
` therefore -2 xx sqrt (6.25) =-2.5 t`
`therefore -2 xx 2.5 =-2.5t`
`therefore t =2` second