Answer
$${\bf{v}}\left( 0 \right) = 2{\bf{j}}$$$${\bf{a}}\left( 0 \right) = - 3{\bf{i}}$$
Work Step by Step
$$\eqalign{
& {\bf{r}}\left( t \right) = 3\cos t{\bf{i}} + 2\sin t{\bf{j}},{\text{ }}\left( {3,0} \right) \cr
& {\text{Let }}t = 0 \cr
& {\bf{r}}\left( 0 \right) = 3\cos \left( 0 \right){\bf{i}} + 2\sin \left( 0 \right){\bf{j}} \cr
& {\bf{r}}\left( 0 \right) = 3{\bf{i}} + 0{\bf{j}} \cr
& {\text{Then, at }}\left( {3,0} \right){\text{ }}t = 0 \cr
& \left( {\bf{a}} \right){\text{Find the vectors: }}{\bf{v}}\left( t \right),{\text{ }}{\bf{a}}\left( t \right){\text{ and speed}}{\text{.}} \cr
& {\bf{v}}\left( t \right) = {\bf{r}}'\left( t \right) \cr
& {\bf{v}}\left( t \right) = \frac{d}{{dt}}\left[ {3\cos t{\bf{i}} + 2\sin t{\bf{j}}} \right] \cr
& {\bf{v}}\left( t \right) = - 3\sin t{\bf{i}} + 2\cos t{\bf{j}} \cr
& {\text{speed}} = \left\| {{\bf{v}}\left( t \right)} \right\| = \left\| { - 3\sin t{\bf{i}} + 2\cos t{\bf{j}}} \right\| \cr
& {\text{speed}} = \sqrt {{{\left( { - 3\sin t} \right)}^2} + {{\left( {2\cos t} \right)}^2}} = \sqrt {9{{\sin }^2}t + 4{{\cos }^2}t} \cr
& {\bf{a}}\left( t \right) = {\bf{v}}'\left( t \right) \cr
& {\bf{a}}\left( t \right) = \frac{d}{{dt}}\left[ { - 3\sin t{\bf{i}} + 2\cos t{\bf{j}}} \right] \cr
& {\bf{a}}\left( t \right) = - 3\cos t{\bf{i}} - 2\sin t{\bf{j}} \cr
& \cr
& \left( {\bf{b}} \right){\text{Evaluating }}{\bf{v}}\left( t \right),{\text{ }}{\bf{a}}\left( t \right){\text{ and speed at the given point}}{\text{.}} \cr
& {\text{At }}\left( {3,0} \right){\text{ }}t = 0 \cr
& {\bf{v}}\left( 0 \right) = - 3\sin \left( 0 \right){\bf{i}} + 2\cos \left( 0 \right){\bf{j}} \cr
& {\bf{v}}\left( 0 \right) = 2{\bf{j}} \cr
& {\text{speed}} = \sqrt {9{{\sin }^2}\left( 0 \right) + 4{{\cos }^2}\left( 0 \right)} \cr
& {\text{speed}} = 2 \cr
& {\bf{a}}\left( 0 \right) = - 3\cos \left( 0 \right){\bf{i}} - 2\sin \left( 0 \right){\bf{j}} \cr
& {\bf{a}}\left( 0 \right) = - 3{\bf{i}} \cr
& \cr
& \left( {\bf{c}} \right){\text{ Sketching}} \cr
& {\bf{r}}\left( t \right) = 3\cos t{\bf{i}} + 2\sin t{\bf{j}} \cr
& x = 3\cos t,{\text{ }}y = 2\sin t \cr
& {\text{Graph}} \cr} $$
