1 min readβ’june 18, 2024

While the title says βOther Than Motion,β 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.Β

1. A population of rabbits and how many are there each year.

- 1st derivative: rabbits/year
- 2nd derivative: rabbits/year squared.Β

2. Liters of Gas filling a tank and how long it takes in hours.Β

- 1st derivative: liters/hour
- 2nd derivative: liters/hour squared.Β

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.Β

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

Browse Study Guides By Unit

πUnit 1 β Limits & Continuity

π€Unit 2 β Fundamentals of Differentiation

π€π½Unit 3 β Composite, Implicit, & Inverse Functions

πUnit 4 β Contextual Applications of Differentiation

β¨Unit 5 β Analytical Applications of Differentiation

π₯Unit 6 β Integration & Accumulation of Change

πUnit 7 β Differential Equations

πΆUnit 8 β Applications of Integration

π¦Unit 9 β Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)

βΎUnit 10 β Infinite Sequences & Series (BC Only)

πStudy Tools

π€Exam Skills

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