Respuesta :
Answer:
It will approximately take 138.89 feet for the car to stop when travelling at 50 mph.
Step-by-step 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:
[tex]d\propto r^2[/tex]
Removing sign of proportionality and adding constant of proportionality, we get,
[tex]d = kr^2[/tex]
When d = 200, r = 60
Putting values, we get,
[tex]200 = k(60)^2\\\\k = \dfrac{200}{3600} = \dfrac{1}{18}[/tex]
Thus, we can write the relation:
[tex]d = \dfrac{r^2}{18}[/tex]
We have to evaluate the stopping distance, d when speed is 50 mph.
Putting r = 50 in the equation, we get,
[tex]d = \dfrac{(50)^2}{18} \approx 138.89[/tex]
Thus, it will approximately take 138.89 feet for the car to stop when travelling at 50 mph.
