Problem: The city is trying to figure out how long the traffic light should stay yellow at an intersection. The speed limit on the road is 45.0 km/h and the intersection is 23.0 m wide. A car is traveling at the speed limit in the positive direction and can brake with an acceleration of 5.20 m/s2.
Part A: If the car is to stop on the white line, before entering the intersection, what is the minimum distance from the line at which the driver must apply the brakes?
Part B: How long should the traffic light stay yellow so that if the car is just closer than that minimum distance when the light turns yellow, it can safely cross the intersection without having to speed up?
Please explain your answer. I know substitution is involved so be sure to give a detailed explanation on that as well.