Freeway Traffic. According to a Scientific American article (May, 1990), current freeways can sustain about N vehicles per lane per hour in smooth traffic flow at speed . Above that figure the traffic flow becomes "turbulent" (stop-and-go).

1) If a vehicle is of length L on the average, what is the average spacing between vehicles at the above traffic density?

2) Collision-avoidance automated control systems, which operate by bouncing radar or sonar signals off surrounding vehicles and then accelerate or brake the car when necessary, could greatly reduce the required spacing between vehicles. If the average spacing is a distance x (two car lengths), how many vehicles per hour can a lane of traffic carry at speed v?