From Mechanics

The expression for the velocity \displaystyle \mathbf{v} was obtained in part a),

\displaystyle \begin{align} & \mathbf{r}=\int{\mathbf{v}dt} \\ & \\ & =\left( 40t+{{d}_{1}} \right)\mathbf{i}+\left( -{{t}^{2}}+{{d}_{2}} \right)\mathbf{j} \\ & \\ & t=0,\ \mathbf{r}=400\mathbf{j}\ \Rightarrow \ {{d}_{1}}=0,\ {{d}_{2}}=400 \\ & \\ & \mathbf{r}=\left( 40t \right)\mathbf{i}+\left( {-{t}^{2}}+400 \right)\mathbf{j} \end{align}