SOLUTION: To stop a moving car takes some time and distance. The stopping distance d of a car after the brakes have been applied varies directly as the square of the speed r. If a car trave
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Question 967192: To stop a moving car takes some time and distance. The stopping distance d of a car after the brakes have been applied varies directly as the square of the speed r. If a car traveling 60 mph can stop in 200 feet, how fast can a car travel and still stop in 72 feet?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if it varies directly as the square of the speed, then d = k * r^2
when d = 200 and r = 60, the formula becomes 200 = k * 60^2.
divide both sides of the equatin by 60^2 and you get 200 / 60^2 = k
simplify to get k = 1/18.
now that you found k, you can use it to solve the problem.
d = 72 and you want to know the speed.
the formula is d = k * r^2
d = 72 and k = 1/18, so the formula becomes 72 = 1/18 * r^2
multiply both sides of the equation by 18 and you get 72 * 18 = r^2
take the square root of both sides of the equation and solve for r to get r = 36 mph.
when the car is traveling at 36 miles per hour, it can stop in 72 feet.
when the car is trveling at 60 miles per hour, it can stop in 200 feet.
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