From Mechanics

Using the result from part b) for the velocity,

\displaystyle \begin{align} & s(20)=\int_{0}^{20}{v}dt \\ & \\ & =\int_{0}^{20}{\left( \frac{{{t}^{2}}}{5}+8 \right)dt} \\ & \\ & =\left[ \frac{{{t}^{3}}}{15}+8t \right]_{0}^{20} \\ & \\ & =\left( \frac{{{20}^{3}}}{15}+8\times 20 \right)-0 \\ & \\ & =693\text{ m} \end{align}