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. (a) ` 2s `
B. (b) ` 4 s`.
C. (c ) `8`
D. (d) ` 1s `

Answer

A

Explanation

` a = (dv)/(dt) =- 2.5 sqrt v `or (dv)/(sqrt v) =- 2.5 dt`
Integratign it with in the conditions as time changes ` 0 ` to ` t`, velocity changes ` 6. 25` m//s ` to zero.
` :. Int _(6. 25)^0 (dv)/sqrt v) =- int _0^t 2.5 dt`
` 2( sqrt v)_(6.25)^0 =- 2. 5 t` or ` - 2 sqrt 6. 25 =- 2.5 t`
or `- 2 xx 2.5 =- 2. 5 t` or ` t=2 s`.