The relation between time $\mathrm{t}$ and distance $\mathrm{x}$ is $\mathrm{t}={\mathrm{ax}}^2+\mathrm{bx}$ where $\mathrm{a}$ and $\mathrm{b}$ are constants. The acceleration is

         $\mathrm{t}={\mathrm{ax}}^2+\mathrm{bx}$

        $\frac{\mathrm{dt}}{\mathrm{dx}}=2\mathrm{ax}+\mathrm{b}$

or    $\frac{\mathrm{dx}}{\mathrm{dt}}={(2\mathrm{ax}+\mathrm{b})}^{-1}$

or    $\mathrm{v}={(2\mathrm{ax}+\mathrm{b})}^{-1}$

Acceleration$=\frac{\mathrm{dv}}{\mathrm{dt}}$

                      $=\frac{\mathrm{dv}}{\mathrm{dx}}·\frac{\mathrm{dx}}{\mathrm{dt}}$

                      $=(-1){(2\mathrm{ax}+\mathrm{b})}^{-2}\left(2\mathrm{a}\right){(2\mathrm{ax}+\mathrm{b})}^{-1}$

                      $=-2\mathrm{a}{(2\mathrm{ax}+\mathrm{b})}^{-3}=-2{\mathrm{av}}^3$