While the title says “Other Than Motion,” really all rates of change are talking about something being in motion. It may not directly say something is in motion but is talking about a change in some way that involved something moving.
Here are some examples, as an activity, think of the units of the first and second derivatives of these situations.
1. A population of rabbits and how many are there each year.
1st derivative: rabbits/year
2nd derivative: rabbits/year squared.
2. Liters of Gas filling a tank and how long it takes in hours.
1st derivative: liters/hour
2nd derivative: liters/hour squared.
You probably get the point!
1st derivative: Measure/time
2nd derivative: Measure/time squared.
Some other situations to apply the rate of change to:
Distance a car travels
People or objects entering or leaving a place
In all these situations, you can use the context to see if the derivative should be positive or negative.
For example, If people are leaving a room, their rate of change would be negative.
What situations would make the rates of change of the other three situations negative?
Rabbits: Population declining (SAD MEME)
Liters of Gas: Gas being used and leaving the tank
The distance a car travels: Car turns around back to where it came
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