Given the displacement equation, $s=\frac{t^2}{4}$

Velocity of the body, $v=\frac{ds}{dt}=\frac{t}{2}$

Acceleration of the body, $a=\frac{dv}{dt}=\frac{1}{2}$

Force on the body, $F=ma=8 \mathrm{kg}\times \frac{1}{2}\mathrm{m} {\mathrm{s}}^{-2}=4 \mathrm{N}$

Work done by the force in first $4$seconds, 

$$\begin{gathered} W=\text{Force}\times \text{ displacement} \\ W=4\times \frac{t^2}{4}=t^2 \\ {\overline{)W}}_{t=0}^{t=4}=16 \mathrm{J} \end{gathered}$$