Determine the constant of variation for the stated condition.
-The distance that an object falls when it is dropped is directly proportional to the square of the amount of time since it was dropped. An object falls 39.2 meters in 2 seconds. Find the distance the object falls in 3 seconds.
A) 88.2 meters
B) 29.4 meters
C) 58.8 meters
D) 6 meters

Question

Quizplus · Accepted Answer

The distance $d$ is directly proportional to the square of the time $t^2$, so $d = kt^2$, where $k$ is the constant of variation. Given $d = 39.2$ meters when $t = 2$ seconds, we find $k = 39.2 / 2^2 = 9.8$. For $t = 3$ seconds, $d = 9.8 \times 3^2 = 88.2$ meters.

Determine the Constant of Variation for the Stated Condition