Halliday, Resnick & Walker — Rotation: Problem Problem_94

Roundabout management. Figure 10.40 shows an overhead view of a single-lane roundabout where access is computer controlled. Car 1 is allowed to enter at access point A at time \(t = 0\). It accelerates at \(a = 3.0 \text{ m/s}^2\) to the speed limit of \(v = 13.4 \text{ m/s}\) as it moves around the roundabout and past access point B where car 2 waits to enter. The radius \(R\) of the circular road is \(45 \text{ m}\), the angle \(\theta\) subtended between A and B is \(120^\circ\), and both cars have length \(L = 4.5 \text{ m}\). Car 2 is allowed to enter when the rear of car 1 is \(2.0\) car lengths past point B. At what time \(t\) is car 2 released?