The kinetic energy acquired by a mass m in traveling a certain distance d, staring from rest, under the action of a constant force is directly proportional to

$$\begin{gathered} \text{ K.E. }=\frac{1}{2}{\mathrm{mv}}^2 \\ \text{ Further, }{\mathrm{v}}^2={\mathrm{u}}^2+2\mathrm{as}\text{ or }{\mathrm{v}}^2=0+2\mathrm{ad} \\ {\mathrm{v}}^2=2(\mathrm{F}/\mathrm{m})\mathrm{d} \\ \text{ Substituting the value of }{\mathrm{v}}^2\text{ from eq. (2) in eq. (1), we get } \\ \text{ K.E. }=\frac{1}{2}\mathrm{m}\times 2(\mathrm{F}/\mathrm{m})\mathrm{d}=\mathrm{Fd} \\ \text{ K.E. }\propto \mathrm{d}\text{ (independent of mass) } \end{gathered}$$