Question

You are driving toward a traffic signal when it turns yellow. Your speed is the legal speed limit of V0 = 55 km/h; your best deceleration rate has the magnitude a = 5.18 m/s². Your best reaction time to begin braking is T = 0.75 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 km/h if the distance to the intersection and the duration of the yellow light are (a) 40 m and 2.8 s, and (b) 32 m and 1.8 s? Give an answer of brake, continue, either (if either strategy works), or neither (if neither strategy works and the yellow duration is inappropriate).

Answer 1

(a) 40 m and 2.8 s. Determine the distance it will take if the driver hits the brake pedal:

$$x=v_0(T+t)-\dfrac{at^2}2=-16\text{ m}$$

Should brake but not that hard.

(b) 32 m and 1.8 s:

$$x=v_0(T+t)-\dfrac{at^2}2=-2.4\text{ m}$$

Should brake but not that hard.