Question

A walnut falls from a tree branch to the ground. The height,
, in feet, of the walnut above the ground is a function of the number of seconds,
, since it started falling.


Which statement provides a correct interpretation of the average rate of change of this function from
to
?

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A.
The average rate of change is
, which means that the walnut fell at a constant speed of 20 feet per second.

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B.
The average rate of change is
, which means that the walnut fell at a constant speed of 40 feet per second.

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C.
The average rate of change is
, which means that the walnut fell the same distance as something moving at a constant speed of 20 feet per second.

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D.
The average rate of change is
, which means that the walnut fell the same distance as something moving at a constant speed of 40 feet per second.

Answer 1

C.

The average rate of change = (change in height)/(change in time) gives the walnut's average vertical velocity over the interval (−20 ft/s in sign, magnitude 20 ft/s), so the walnut fell the same distance over that time as an object moving at a constant 20 ft/s. It does not mean the walnut's speed was constant during the fall.