From Mechanics

In this case we have \displaystyle \mathbf{u}=0 , \displaystyle \mathbf{a}=2\mathbf{i}+3\mathbf{j} and \displaystyle {{\mathbf{r}}_{0}}=0.

Substituting these into the equation \displaystyle \mathbf{v}=\mathbf{u}+\mathbf{a}t \ \ gives the velocity of the body at time \displaystyle t=4 \text{ s } as:

\displaystyle \mathbf{v}=0+(2\mathbf{i}+3\mathbf{j})\times 4

which gives

\displaystyle \mathbf{v}=8\mathbf{i}+12\mathbf{j} \ \text{ m}{{\text{s}}^{\text{-1}}}

Then substituting the above into the equation \displaystyle \mathbf{r}=\mathbf{u}t+\frac{1}{2}\mathbf{a}{{t}^{\ 2}}+{{\mathbf{r}}_{0}} gives the position vector of the body at time \displaystyle t=4 \text{ s } as:

\displaystyle \begin{align} & \mathbf{r}=0\times 4+\frac{1}{2}(2\mathbf{i}+3\mathbf{j})\times {{4}^{\ 2}}+0 \\ & =16\mathbf{i}+24\mathbf{j} \ \text{m} \end{align}