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.