a
From qusestion, \(v = a\sqrt s  = \frac{{ds}}{{dt}}\)

or,   \(\begin{gathered}
  2\sqrt s \,\,\, = at \Rightarrow s = \frac{{{a^2}{t^2}}}{4} \hfill \\
  \,\,\,\,\,\,\,\,\,\,\,\,\,\,F = m \times \frac{{{a^2}}}{2} \hfill \\ 
\end{gathered} \)

Work done \(=\frac{{m{a^2}}}{2} \times \frac{{{a^2}{t^2}}}{4} = \frac{1}{8}m{a^4}{t^2}\)