From Mechanics

Using the result for the velocity obtained in part a)

\displaystyle \begin{align} & s(50)=\int_{0}^{50}{v}dt \\ & \\ & =\int_{0}^{50}{\left( \frac{{{t}^{2}}}{50}+2 \right)dt} \\ & \\ & =\left[ \frac{{{t}^{3}}}{150}+2t \right]_{0}^{50} \\ & \\ & =\left( \frac{{{50}^{3}}}{150}+2\times 50 \right)-0 \\ & \\ & =933\text{ m} \end{align}