An object’s velocity vector, $\vec{v}$, is given by $\vec{v} = (2 + \pi \sin(\pi ))\vec{i} + 2\vec{j}.$
Find its position vector, $\vec{r}$, with initial condition, $t = 0, \vec{r} = −\vec{i}+\vec{j}$.
How can I do this question? Do I have to replace t=o in vector $\vec{v}$? and dot product with $\vec{r}$? any help, please.
Hint
This is a vectorial differential equation. You just have to integrate coordinate by coordinate. Taking into account the initial vector.