$$\begin{gathered} \mathrm{t}=\sqrt{\frac{\mathrm{x}+\mathrm{a}}{\mathrm{b}}} \\ \Rightarrow (\mathrm{x}+\mathrm{a})={\mathrm{bt}}^2 \\ \Rightarrow \mathrm{x}=-\mathrm{a}+{\mathrm{bt}}^2 \end{gathered}$$

Comparing this equation with general equation of uniformly accelerated motion, $\mathrm{s}={\mathrm{s}}_{\mathrm{i}}+\mathrm{ut}+\frac{1}{2}{\mathrm{at}}^2$

we see that ${\mathrm{s}}_{\mathrm{i}}=-\mathrm{a}, \mathrm{u}=0$ and acceleration = 2b.