SOLUTION: Dear Algebra.com tutors, I'm stumped! Can you help with this bonus problem? How long would a yellow light have to remain lit to allow a car to safely stop before reaching a

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Question 154640: Dear Algebra.com tutors,
I'm stumped! Can you help with this bonus problem?
How long would a yellow light have to remain lit to allow a car to safely stop before reaching a 100 ft intersection if the car is traveling at a rate of 50 mph when it begins to decelerate at a steady rate of -20 ft/second squared, after a reaction time of 0.6 seconds?
Use the following two physics formulas to aid in solving this problem:
x = v-subzero * t + 1/2 * a * t-squared
and
v-squared = v-subzero squared + 2 * a * x
(x = distance, a = acceleration, v = velocity, t = time, v-subzero = initial velocity)
Thanks for trying! I appreciated it!
Sam
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
50 mph multiplied by 5280 ft per mi and divided by 3600 sec per hr gives 220/3 fps

with a deceleration of 20 fps^2, it takes 11/3 ([220/3]/20) sec to decelerate to a stop

adding the .6 sec reaction time gives a total stopping time of 4.27 sec (approx)

the car travels 44 ft ([220/3]*.6) during the reaction time
__ and [(220/3)/2]*(11/3) or 134.4 ft (approx) during deceleration

for a total stopping distance of 178.4 ft (approx)