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 v_0 = 55 km/h; your best deceleration rate has the magnitude a = 5.18 m/s^2. 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) 38 m and 2.7 s, and (b) 32 m and 1.5 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

first convert velocity:
55km/h * 1000m/km * 1h/3600s = 15.3 m/s

try to stop: reaction distance s = 15.2m/s * 0.75s = 11.5m
braking distance: v² = 0 = u² + 2as = (15.3m/s)² - 2 * 5.12m/s² * s
s = 233m²/s² / 10.24m/s² = 22.8 m
combined distance = 34.3 m

continue at pace:
(a) s = 15.3m/s * 2.7s = 41.32 m (I'll consider this legal)
(b) s = 15.3m/s * 1.5s = 22.96 m (not legal)

So, case A: either
and case B: neither

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