Question

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?

Answer 1

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.