Answer
The two parametrizations trace the same curve, however as is shown in the figure attached, only the velocity vectors point in the same direction. Since the $x$- and $y$-component of ${{\bf{r}}_1}\left( t \right)$ increase faster than ${\bf{r}}\left( t \right)$, we expect the velocity vector and acceleration vector of ${{\bf{r}}_1}\left( t \right)$ have larger magnitude.
$\begin{array}{*{20}{c}}
t&{{\bf{v}}\left( t \right)}&{{{\bf{v}}_1}\left( t \right)}&{{\bf{a}}\left( t \right)}&{{{\bf{a}}_1}\left( t \right)}\\
{}&{\left( {2t,3{t^2}} \right)}&{\left( {4{t^3},6{t^5}} \right)}&{\left( {2,6t} \right)}&{\left( {12{t^2},30{t^4}} \right)}\\
1&{\left( {2,3} \right)}&{\left( {4,6} \right)}&{\left( {2,6} \right)}&{\left( {12,30} \right)}
\end{array}$
Work Step by Step
We have ${\bf{r}}\left( t \right) = \left( {{t^2},{t^3}} \right)$ and ${{\bf{r}}_1}\left( t \right) = \left( {{t^4},{t^6}} \right)$. The two parametrizations trace the same curve, however as is shown in the figure attached, only the velocity vectors point in the same direction. Since the $x$- and $y$-component of ${{\bf{r}}_1}\left( t \right)$ increase faster than ${\bf{r}}\left( t \right)$, we expect the velocity vector and acceleration vector of ${{\bf{r}}_1}\left( t \right)$ have larger magnitude.
The velocity vectors:
${\bf{v}}\left( t \right) = {\bf{r}}'\left( t \right) = \left( {2t,3{t^2}} \right)$, ${\ \ }$ ${{\bf{v}}_1}\left( t \right) = {{\bf{r}}_1}'\left( t \right) = \left( {4{t^3},6{t^5}} \right)$
So, ${\bf{v}}\left( 1 \right) = \left( {2,3} \right)$ and ${{\bf{v}}_1}\left( 1 \right) = \left( {4,6} \right)$.
The acceleration vectors:
${\bf{a}}\left( t \right) = {\bf{r}}{\rm{''}}\left( t \right) = \left( {2,6t} \right)$, ${\ \ }$ ${{\bf{a}}_1}\left( t \right) = {{\bf{r}}_1}{\rm{''}}\left( t \right) = \left( {12{t^2},30{t^4}} \right)$
So, ${\bf{a}}\left( 1 \right) = \left( {2,6} \right)$ and ${{\bf{a}}_1}\left( 1 \right) = \left( {12,30} \right)$
In summary:
$\begin{array}{*{20}{c}}
t&{{\bf{v}}\left( t \right)}&{{{\bf{v}}_1}\left( t \right)}&{{\bf{a}}\left( t \right)}&{{{\bf{a}}_1}\left( t \right)}\\
{}&{\left( {2t,3{t^2}} \right)}&{\left( {4{t^3},6{t^5}} \right)}&{\left( {2,6t} \right)}&{\left( {12{t^2},30{t^4}} \right)}\\
1&{\left( {2,3} \right)}&{\left( {4,6} \right)}&{\left( {2,6} \right)}&{\left( {12,30} \right)}
\end{array}$
