Chapter 02, Problem 040 You are driving toward a traffic signal when it turns ye

Question

Chapter 02, Problem 040 You are driving toward a traffic signal when it turns yellow. Your speed is the legal speed limit of vo - 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) 37 m and 2.8 s, and (b) 32 m and 1.6 s? Give an answer of brake, continue, either (if either strategy works), or neither (if neither strategy works and the yellow duration is inappropriate).

Explanation / Answer

v0 = 55 km/h = 55*1000/3600 = 15.28 m/s

a) dcontinue = 15.28*2.8 = 42.8 m

here a = -5.18 m/s^2

d coast = 15.28*0.75 = 11.5 m

x = d brake = (vf^2-v0^2)/2a = -15.28^2/2*(-5.18) = 22.5 m

d tot = 11.5+22.5 = 34 m

either strategy works

b) d continue = 15.28/1.6 = 9.55 m

Continuing does not work, since the distance is needed 32 m

d tot = 34 m

breaking does not working neither strategy works

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