Traffic signals: The number of seconds n for the yellow light is critical to safety at a traffic signal. One study recommends a formula for setting the time that permits a driver who sees the yellow...

Traffic signals: The number of seconds n for the yellow light is critical to safety at a traffic signal. One study recommends a formula for setting the time that permits a driver who sees the yellow light shortly before entering the intersection either to stop the vehicle safely or to cross the intersection at the current approach speed before the end of the yellow light.69 For a street of width 70 feet under standard conditions, the formula is

Here v is the approach speed in feet per second. (See Figure 5.127.)

a. Make a graph of n as a function of v. Include speeds from 30 to 80 feet per second (roughly 20 to 55 miles per hour).

b. Express using functional notation the length of the yellow light when the approach speed is 45 feet per second, and then calculate that value.

c. Explain in practical terms the behavior of the graph near the pole at v = 0.

d. What is the minimum length of time for a yellow light?