Answer
a) $\textbf{v}(t) = <6t, 8t>$; Speed = $10t$
b) $\textbf{a}(t) = <6, 8>$
Work Step by Step
$\textbf{r}(t) = <3t^2 +1, 4t^2+3>$
$\textbf{v}(t) = \textbf{r}'(t) = <6t, 8t>$
Speed = $|\textbf{v}(t)| = \sqrt {(6t)^2+(8t)^2} = 10t$
$\textbf{a}(t) = \textbf{v}'(t) = <6, 8>$