Figure $2-42$ shows part of a street where traffic flow is to be controlled to allow a platoon of cars to move smoothly along the street. Suppose that the platoon leaders have just reached intersection 2 , where the green appeared when they were distance $d$ from the intersection. They continue to travel at a certain speed $v_{p}$ (the speed limit) to reach intersection 3 , where the green appears when they are distance $d$ from it. The intersections are separated by distances $D_{23}$ and $D_{12}$. (a) What should be the time delay of the onset of green at intersection 3 relative to that at intersection 2 to keep the platoon moving smoothly?
Suppose, instead, that the platoon had been stopped by a red light at intersection 1. When the green comes on there, the lcaders require a certain time $t_{r}$ to respond to the change and an additional time to accelerate at some rate $a$ to the cruising speed $v_{p}$. (b) If the green at intersection 2 is to appear when the leaders are distance $d$ from that intersection, how long after the light at intersection 1 turns green should the light at intersection 2 turn green?