An automobile accelerates from rest at \(t=0\) such that its tires undergo a constant rotational acceleration \(\alpha=5.8 \mathrm{~s}^{-2}\). The radius of each tire is \(0.33 \mathrm{~m}\). At \(t=10 \mathrm{~s}\), compute \((a)\) the rotational speed \(\omega\) of the tires, \((b)\) the rotational displacement \(\Delta \vartheta\) of each tire, \((c)\) the speed \(v\) of the automobile (assuming the tires stay perfectly round), and

(d) the distance it has traveled.