Sol. $t=\alpha x^2+\beta x$ (differentiating wrt time) $$ \begin{aligned} & \frac{\mathrm{dt}}{\mathrm{dx}}=2 \alpha \mathrm{x}+\beta \\ & \frac{1}{\mathrm{v}}=2 \alpha \mathrm{x}+\beta \end{aligned} $$ (differentiating wit time) $$ \begin{aligned} & -\frac{1}{\mathrm{v}^2} \frac{\mathrm{dv}}{\mathrm{dt}}=2 \alpha \frac{\mathrm{dx}}{\mathrm{dt}} \\ & \frac{\mathrm{dv}}{\mathrm{dt}}=-2 \alpha \mathrm{v}^3 \end{aligned} $$