### Kinematics

(a) The velocity is given by
$\frac{d\vec{r}}{dt} = \frac{d}{dt}(A\hat{i})+\frac{d}{dt}(Bt^{2}\hat{j})+\frac{d}{dt}(Ct\hat{k})$

$\hat{v} = 0+2Bt\hat{j}+C\hat{k}$
(b)The acceleration is\begin
$\frac{d\vec{v}}{dt} = \frac{d}{dt}(2Bt\hat{j})+\frac{d}{dt}(C\hat{k})$
$\vec{a} = 0+2B\hat{j}+0$
(c) Nothing interesting happens in the x direction so we look at the
yz plane. The path in this plane is a parabola.