Solve the variation problem.
-The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 60 miles per hour?
A)252 feet
B)252.34 feet
C)216 feet
D)264.3 feet

Question

Quizplus · Accepted Answer

The stopping distance $d$ varies directly as the square of the speed $v$, so we can write $d = kv^2$, where $k$ is a constant. Given $d = 112$ feet at $v = 40$ mph, we can find $k$ and then use it to find the stopping distance at $60$ mph. For $40$ mph, $112 = k(40)^2$, solving for $k$ gives $k = 112 / 1600 = 0.07$. For $60$ mph, $d = 0.07(60)^2 = 0.07(3600) = 252$ feet.

Solve the Variation Problem