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 $x = \mathrm { d }$, will be :\\
(1) $\frac { m } { 2 \alpha ^ { 2 } d }$\\
(2) $\frac { \mathrm { md } } { 2 \alpha ^ { 2 } }$\\
(3) $2 m \alpha ^ { 2 } d$\\
(4) $\frac { m \alpha ^ { 2 } d } { 2 }$