A particle of mass $$m$$ moves on a straight line with its velocity increasing with distance according to the equation $$v = \alpha\sqrt{x}$$, where $$\alpha$$ is a constant. The total work done by all the forces applied on the particle during its displacement from $$x = 0$$ to $$x = d$$, will be :

A

$$\frac{m}{2\alpha^2 d}$$

B

$$\frac{md}{2\alpha^2}$$

C

$$2m\alpha^2 d$$

D

$$\frac{m\alpha^2 d}{2}$$