A train starts from rest at $S=0$ and is subjected to an acceleration as shown in figure.

$a-s$ equation corresponding to given graph is,

                                     $a=6-\frac{s}{5}$

$\therefore$ $v.\frac{dv}{ds}=\left(6-\frac{s}{5}\right)$ or   ${\int }_0^{v}vdv={\int }_0^s\left(6-\frac{s}{5}\right)ds$

or                                   $v=\sqrt{125-\frac{s^2}{5}}$

At                                   $s=10 \mathrm{m}, v=10 \mathrm{m}/\mathrm{s}$

Also $\frac{v^2}{125}+\frac{S^2}{625}=1$ which represents an ellipse.