Acceleration: Why Is Distance the Square of Time?

(This module is intended to follow a discussion of the constant acceleration of a free-falling object.)

For a free-falling object, you can calculate the total distance traveled, given the amount of time. It turns out that distance of the fall is proportional to the square of the time elapsed. (The actual equation is: d = vi*t + 1/2 * a * t2)

You may wonder, what does squaring time have to do with anything? The animation below depicts this relationship. (We are simplifying the math by rounding up gravity's rate of acceleration from 9.8 m/s to 10 m/s.)

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