Constant & Varying Rates of Change

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

A rate of change measures how quickly a measured quantity is changing. In this lesson, learn about rates of change and how to tell if a rate of change is constant or varying.

What is a Rate of Change?

Get up and walk across the room. Did your position change? Of course it did! You are on the other side of the room now. How quickly did your position change? That depends on how quickly you were walking, right? The speed at which you walked is an example of a rate of change. In this case, you are measuring the rate of the change of your position, but in general, a rate of change measures how quickly a certain quantity (like your position) is changing.

Constant Rate of Change

When you walk without slowing down or speeding up at all, then the rate of change of your position is constant. This means that if you travel 2 meters in the first second, you travel 2 meters in the second second, and 2 meters in the third second, and so on until you decide to stop walking. Each second you travel the exact same distance, so your position is changing at exactly the same rate all the time.

If you move the same distance each second, then your position is changing at a CONSTANT rate
rate of change of position

One way to determine if a rate of change is constant or not is to plot the quantity you are measuring on a graph. If you made a graph of your position vs. time as you walked across the room, it would look something like this:


position vs. time graph


Looking at the graph above, you probably noticed that the points form a straight line. This straight line indicates that the rate of change of the quantity being measured (your position) is constant.

We can find out even more about the rate of change from a graph like this. You can calculate the slope of the line to get the rate of change of your position, which is your speed. Each second, your position changes by 2 meters, so your speed is 2 meters per second.


 slope of a position time graph


Varying Rate of Change

If you move at exactly the same speed as you walk across the room, then the rate of change of your position will be constant and a graph of your position vs. time will form a straight line. What happens if you DON'T move at a constant speed, though? What if you speed up?

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