You are driving toward a traffic signal when it turns yellow. Your speed is the

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) 36 m and 2.9 s, and (b) 30 m and 1.7 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

Given u = 55 km/hr = 55 x 1000/3600 = 15.28 m/s
Let you are (at reaction distance) meter away from the light
=>distance traveled in reaction time = 0.75 x 15.28 = 11.46 m
Let you stop in t sec after the reaction time
=>v = u -at
=>0 = 15.28 - 5.18 x t
=>t = 2.95 sec
By s = ut - 1/2at^2
=>s = 15.28 x 2.95 - 1/2 x 5.18 x (2.95)^2
=>s = 22.54 m
=>Total distance to stop = s + reaction distance = 22.54 + 11.46 = 34 m
=>Total time to stop = 2.95 + 0.75 = 3.70 sec

Case 1) 36 and and 2.9 sec   in this case you win because 36-34 = 2mtr and 3.7-2.95 = 1.15 sec

Case 2: 30 and 1.7 sec   so 30 -34 = 4 mtrs beyond line you loose

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