Answer
$16.3\,m/s$
Work Step by Step
We're given $\vec{r}(t) = 3t\,\hat{i}-4t^2\hat{j}+2\,\hat{k}$.
We know the velocity is the derivative of the displacement vector. We can thus find $\vec{v}$ by taking derivatives of $\vec{r}$ component-wise:
$\vec{v}(t) = 3\,m/s\,\hat{i}-(8\,m/s^2\,)t\hat{j}$.
Now we can plug in $t=2\,s$ to obtain:
$\vec{v}_{(2)} = 3\,m/s\,\hat{i}-16\,m/s\,\hat{j}$.
The magnitude is (by the Pythagorean theorem):
$\sqrt{(3\,m/s)^2+(-16\,m/s)^2} = 16.3\,m/s$.
