Answer
Please see the figure attached.
The velocity and acceleration vectors at $t=1$:
${\bf{v}}\left( 1 \right) = \left( {2,3} \right)$
${\bf{a}}\left( 1 \right) = \left( {2,6} \right)$
Work Step by Step
We have ${\bf{r}}\left( t \right) = \left( {{t^2},{t^3}} \right)$.
The velocity vector:
${\bf{v}}\left( t \right) = {\bf{r}}'\left( t \right) = \left( {2t,3{t^2}} \right)$
So, ${\bf{v}}\left( 1 \right) = \left( {2,3} \right)$.
The acceleration vector:
${\bf{a}}\left( t \right) = {\bf{r}}{\rm{''}}\left( t \right) = \left( {2,6t} \right)$
So, ${\bf{a}}\left( 1 \right) = \left( {2,6} \right)$.
