A particle of mass m moves on a straight line with its velocity varying with the distance travelled according to the equation `v=asqrtx`, wher ea is a constant. Find the total work done by all the forces during a displacement from `x=0 to x=d`.

Options

A. `(mad)/(2)`
B. `(mad^2)/(d)`
C. `(ma^2d)/(2)`
D. `(m^2ad)/(2)`

Answer

C

Explanation

`v=asqrtx`
`x=0`,`v_1=0`
`x=d`,`v_2=asqrtd`
`W_(1rarr2)=K_2-K_1=(1)/(2)m(v_2^2-v_1^2)`
`=(1)/(2)m(ad-0)=(1)/(2)ma^2d`