Traffic signals: The number of seconds n for the yellow light is critical to safety at a traffic signal. One study6 recommends the following formula for setting the time:
Here t is the perception-reaction time of a driver in seconds, v is the average approach speed in feet per second, a is the deceleration rate in feet per second per second, w is the crossing-street width in feet, and l is the average vehicle length in feet. If we assume that the average perception-reaction time is 1 second, the approach velocity is 40 miles per hour (58.7 feet per second), the deceleration rate is 15 feet per second per second, and the average vehicle length is 20 feet, then n can be expressed as the following linear function of crossing-street width:
a. Under the given assumptions, what is the minimum time the yellow light should be on, no matter what the width of the crossing street?
b. If the crossing street for one signal is 10 feet wider than the crossing street for another signal, how should the lengths of the yellow light times compare?
c. Calculate n(70) and explain in practical terms what your answer means.
d. What crossing-street width would warrant a 5- second yellow light?