Answer
The object makes 9.5 revolutions during the first 4 seconds.
Work Step by Step
The change in angular position is equal to the area under the angular velocity versus time graph. Note that the area under the graph from t = 0 to t = 4 s is 60 rad.
Therefore, $\theta = 60~rad$
We can convert $\theta$ to revolutions.
$\theta = (60~rad)(\frac{1~rev}{2\pi~rad})$
$\theta = 9.5~rev$
The object makes 9.5 revolutions during the first 4 seconds.
