From Mechanics

The expression for the velocity \displaystyle \mathbf{v} has been obtained in part b),

\displaystyle \begin{align} & \mathbf{r}=\int{\mathbf{v}}dt \\ & \\ & =\left( \frac{{{t}^{3}}}{2}-8t+{{d}_{1}} \right)\mathbf{i}+\left( \frac{3{{t}^{2}}}{4}-\frac{5{{t}^{3}}}{24}+{{d}_{2}} \right)\mathbf{j} \\ & \\ & t=0,\ \mathbf{r}=90\mathbf{i}+20\mathbf{j}\ \Rightarrow \ {{d}_{1}}=90,\ {{d}_{2}}=20 \\ & \\ & \mathbf{r}=\left( \frac{{{t}^{3}}}{2}-8t+90 \right)\mathbf{i}+\left( \frac{3{{t}^{2}}}{4}-\frac{5{{t}^{3}}}{24}+20 \right)\mathbf{j} \end{align}