A yellow (amber?) traffic light typically forces drivers to decide, is it safer to drive through the intersection or is it safer to stop at the light? We will first assume that the driver does not try to move faster once a yellow light is observed. In Indiana, a yellow light is on for 3.00 seconds before the red light comes on. For argument sake, assume it takes about 0.5 seconds to decide whether you should hit the brakes or not. The car will continue traveling forward during the period when you are deciding whether to stop or not. The maximum breaking acceleration for this car is approximately g = 7.8- and the width of the intersection is xw = 9.14m. 111 1000 a) Suppose you are traveling at an initial velocity of V. Find a formula for the maximum distance you can be away from the intersection when the light turns yellow and safely pass through the intersection without ever breaking. This formula should only have the initial velocity as a variable. Explain/Show how you arrived at this formula. b) Suppose you are traveling at an initial velocity of V. Find a formula for the minimum distance you can be away from the intersection when the light turns yellow and safely come to a stop (without entering the intersection). This formula should only have the initial velocity as a variable. Explain/Show how your arrived at this formula. c) On the same graph plot the maximum distance (from part a) vs. vo and the minimum distance (from part b) vs. vo (HAND DRAWN GRAPHS ARE NOT ACCEPTABLE; USE A COMPUTER TO DO THIS). Using this graph, are there initial velocities and distances (from the car to the light when it turns yellow) when one can either stop or pass through safely? Using this graph, are there velocities and distances (from the car to the light when it turns yellow) when one can neither stop nor pass through the intersection safely? EXPLAIN NOTE: Despite what we regularly see, Indiana Law says that you MUST make it completely through the intersection before the light turns red or possibly face a traffic ticket.