Answer
$(19\hat{i} - 224\hat{j})\,m/s$
Work Step by Step
We're given $\vec{r}(t) = (2t^3-5t)\hat{i} + (6-7t^4)\hat{j}$, where $\vec{r}(t)$ is in meters.
We know that the velocity vector is the derivative of the position vector. We can thus take derivatives of $\vec{r}(t)$ component-wise to obtain $\vec{v}(t)$:
$\vec{v}(t) = (6t^2-5)\hat{i} - 28t^3\hat{j}$, where $\vec{v}(t)$ is in meters per second.
We can plug in $t=2\,s$ to obtain:
$\vec{v}(2) = ((6*2^2-5)\hat{i} -28*2^3\,\hat{j})\,m/s = (19\hat{i} - 224\hat{j})\,m/s$.
