Question

If we drop a rock near the surface of Earth, its velocity increases by 32 feet per second for each second the rock falls. Is the velocity of the rock a linear function of the time since it was dropped?

Answer 1

The velocity of the rock is the number of feet traveled per second

The velocity of the rock is a linear function of time

How to determine the function?

From the question, we understand that the velocity increases by 32 feet per second for each second

This means that we have the following rates:

Velocity = 0, 32, 64, 96, 128....

Notice that the difference between adjacent numbers is 32.

This means that the velocity changes at a constant rate or slope

Hence, the velocity of the rock is a linear function

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