Differentiate parametric curves and integrate vector motion
Use exact values
For t≥0, acceleration is in m/s², velocity in m/s and position in m. Integrate using both initial vector conditions. Give the three position and velocity components at T
\[\mathbf a(t)=\begin{pmatrix}6\\12t\\-2\end{pmatrix}\]
\[\mathbf v(0)=\begin{pmatrix}2\\-1\\3\end{pmatrix},\quad\mathbf r(0)=\begin{pmatrix}-3\\-2\\-2\end{pmatrix},\quad T=3\]