The problem is as follows:
In the figure from below it is shown an observer who has put himself at the center of the coordinate system. He sees an object moving in a circular trajectory. If the average speed between $A$ and $B$ is $\left ( -2\hat{i}+\hat{j} \right )\frac{m}{s}$ and its position on point $A$ is $5\hat{i}\,m$. Find on $\frac{rad}{s}$ the average angular velocity between $A$ and $B$ if the time the object takes to get from $A$ to $B$ is $4\,s$.
The alternatives on my book:
$\begin{array}{ll} 1.&0.35\hat{k}\\ 2.&0.5\hat{k}\\ 3.&0.55\hat{k}\\ 4.&0.6\hat{k}\\ 5.&0.75\hat{k}\\ \end{array}$
For this particular problem I'm stuck at how to use the information given the average velocity and the position. However I recall that when the word average is mentioned it mean this formula?
$\overline{v}=\frac{\vec{r}}{\Delta t}$
But other than that I'm not sure if it applies in this situation. Can somebody offer some help with this question?.
After 4s the object has moved $-8i+4j$ to $(-3,4)$ and so it has travelled through an angle of $\pi - tan^{-1}(\frac{4}{3})$ in 4s. This is $0.55 s^{-1}$ and so the answer is (3.).