A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v=α √ x, where α is a constant.…

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