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The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car travelling 60 mph can stop in 200 ​ft, how many feet will it take the same car to stop when it is travelling 50 ​mph?

User Kiamoz
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1 Answer

6 votes

Answer:

It will approximately take 138.89 feet for the car to stop when travelling at 50 mph.

Explanation:

We are given the following in the question:

"The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r"

Thus, we can write:


d\propto r^2

Removing sign of proportionality and adding constant of proportionality, we get,


d = kr^2

When d = 200, r = 60

Putting values, we get,


200 = k(60)^2\\\\k = (200)/(3600) = (1)/(18)

Thus, we can write the relation:


d = (r^2)/(18)

We have to evaluate the stopping distance, d when speed is 50 mph.

Putting r = 50 in the equation, we get,


d = ((50)^2)/(18) \approx 138.89

Thus, it will approximately take 138.89 feet for the car to stop when travelling at 50 mph.

User Kailash Yadav
by
7.8k points
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