$A$ 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
  $\frac{m \alpha^2 d}{2}$
• D
  $2 m \alpha^2 d$