Answer
a) The car's average angular speed $\overline\omega=0.33rad/s$
b) The radius of the track $r=128m$
Work Step by Step
We know $t=18.9s$ and $\overline{v_T}=42.6m/s$
a) The distance traveled by the auto race, which is also the total length of one lap, is $$s=t\overline{v_T}=805.14m$$
$s$ is, in fact, the perimeter of the car's rotation circle, whose radius can be found: $$r=\frac{s}{2\pi}=128m$$
The car's average angular speed is $$\overline\omega=\frac{\overline{v_T}}{r}=0.33rad/s$$
b) The radius of the track is $r=128m$
