Differentiation of Vectors

Position Vector

$$ \vec{r}(t) = x(t)\hat{i} + y(t)\hat{j} + z(t)\hat{k} $$

Velocity

$$ \vec{v} = \frac{d\vec{r}}{dt} $$

Acceleration

$$ \vec{a} = \frac{d^2 \vec{r}}{dt^2} $$