Answer
It will take a time of $2\pi$ seconds to go around the whole circle.
Work Step by Step
The radius of the circle is 1 unit. The distance $d$ around the whole circle is $2\pi$ units.
The speed $v$ is 1 unit/s
We can find the time to go around the whole circle:
$t = \frac{d}{v}$
$t = \frac{2\pi~units}{1~unit/s}$
$t = 2\pi~s$
It will take a time of $2\pi$ seconds to go around the whole circle.