The yellow caution light on a traffic signal should stay on long enough to allow a driver to either pass through the intersection or safely stop before reaching the intersection. A car can stop if its distance from the intersection is greater than the stopping distance found in the previous problem. If the car is less than this stopping distance from the intersection, the yellow light should stay on long enough to allow the car to pass entirely through the intersection.
(a) Show that the yellow light should stay on for a time interval ∆ttight = ∆t r – (vo / 2a) + (si / vo) Where ∆tr is the driver’s reaction time, v0 is the velocity of the car approaching the light at the speed limit, a is the braking acceleration, and si is the width of the intersection.
(b) As city traffic planner, you expect cars to approach an intersection 16.0 m wide with a speed of 60.0 km/h. Be cautious and assume a reaction time of 1.10 s to allow for a driver’s indecision. Find the length of time the yellow light should remain on. Use a braking acceleration of - 2.00 m/s2.