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

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).