\(ds = \frac{t}{2}dt\)

\(F = ma = \frac{{m{d^2}s}}{{d{t^2}}} = \frac{{6{d^2}}}{{d{t^2}}}\left[ {\frac{{{t^2}}}{4}} \right]\; = \;3N\)

Now \(W = \int_0^2 {F\,ds} = \int_0^2 {3\frac{t}{2}dt} = \frac{3}{2}\left[ {\frac{{{t^2}}}{2}} \right]_0^2 = \frac{3}{4}\left[ {{{(2)}^2} - {{(0)}^2}} \right] = 3J\)