Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 40

You are driving toward a traffic signal when it turns yellow. Your speed is the legal speed limit of \(v_0 = 55 \text{ km/h}\); your best deceleration rate has the magnitude \(a = 5.18 \text{ m/s}^2\). Your best reaction time to begin braking is \(T = 0.75 \text{ s}\). To avoid having the front of your car enter the intersection after the light turns red, should you brake to a stop or continue to move at \(55 \text{ km/h}\) if the distance to the intersection and the duration of the yellow light are (a) \(40 \text{ m}\) and \(2.8 \text{ s}\), and (b) \(32 \text{ m}\) and \(1.8 \text{ s}\)? Give an answer of brake, continue, either (if either strategy works), or neither (if neither strategy works and the yellow duration is inappropriate).