A body at rest is acted upon by a force $F$ such that it acquires a speed $\text{'}v\text{'}$ while moving with an acceleration $\text{'}a\text{'}$. Show that work done by force on the body is given by $\frac{\mathit{1}}{\mathit{2}}\left(\frac{\mathit{F}}{\mathit{a}}\right)v^{\mathit{2}}\mathit{.}$

A block of mass $30 \mathrm{kg}$is pulled up a slope with a constant speed by applying a force of $200 \mathrm{N}$parallel the slope. $\mathrm{A}$ and $\mathrm{B}$ are initial and final positions of block. Calculate work done by the force in moving the block from $\mathrm{A}$ to $\mathrm{B}$. Also, calculate $\mathrm{P}.\mathrm{E}.$ gained by block.

A body $A$ of mass $20 \mathrm{kg}$ is moving with a velocity of $1 {\mathrm{ms}}^{-1}$ another body $B$ of mass $1 \mathrm{kg}$ is moving with a velocity of $20 {\mathrm{ms}}^{-1}.$ Find the ratio of $\mathrm{K}.\mathrm{E}$ of $A$ and $B\mathit{.}\mathit{ }$