A point moves linearly with deceleration which is given by `dv//dt=-alphasqrt(v)`, where alpha is a positive constant. At the start `v=v_(0)`. The distance traveled by particle before it stops will be

Options

A. `v_(0)^(3//2)/(3alpha)`
B. `(4v_(0)^(3//2))/alpha`
C. `(4v_(0)^(3//2))/(3alpha)`
D. `(2v_(0)^(3//2))/(3alpha)`

Answer

D

Explanation

`(dv)/(dt)=v(dv)/(dx)=-alpha v^(1//2)`
`int_(v_(0))^(v)v^(1//2)dv=-alphaint_(0)^(x) dx`
`(|v^(3//2)|_(v_(0))^(v))/(3/2)=-alphax`
When particle stops, `v=0`
`x=(2 v_(0)^(3//2))/(3alpha)`