Question

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. ` 4 s`
C. 8 s`
D. 1 s`

Answer 1

Correct Answer - A
` (dv /(dt) = - 2.5 sqrt(v) rArr (dv)/(sqrt(v)) = - 2.5 dt `
integrating , ` int _(6.25)^(0) v (-1/2)(dv) = -2.5 int _(0)^(t) dt `
rArr ` [ ( v^(+1/2 ))/((1/2))]_(6.25)^(0) = - 2.5 [ t ] _(0)^(t) `
`rArr - 2 (6.25)^(1/2) = - 2.5t rArr t = 2 sec`