Rate of Change vs. Negative Rate of Change

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  • 0:03 What Is a Rate of Change?
  • 2:02 Positive vs Negative…
  • 3:04 Graphing Rates of Change
  • 3:56 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

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

A rate of change tells you how quickly a quantity is changing. In this lesson, learn about how rates of change are calculated and what it means for a rate of change to be negative.

What Is a Rate of Change?

When you are driving your car, your speedometer tells you how fast you are going at any time. You may not have thought of it before, but the velocity of your car is a rate of change. In this case, it is the rate of change of your car's position. A rate of change describes how much one variable changes in relation to another, and velocity is a great example of a rate of change because your position and time are both changing. If we were to make a graph of your car's position over the time you were driving, it might look something like this:

Position Time Graph

The slope of a line on a graph is always equal to the rate of change of the variable plotted on the y-axis with respect to the variable plotted on the x-axis. You can see on the graph, position is plotted on the y-axis and time is plotted on the x-axis, so the rate of change will tell you how quickly the position of the car changes.

To find the slope of a line, pick two points on the line and calculate the change in the y variable divided by the change in the x variable. In this case, let's choose the points (1 s, 10 m) and (6 s, 60 m). The slope is equal to the change in y over the change in x. Let's go ahead and calculate:

example of slope calculation

So, the slope of this line is your velocity, 10 m/s. Although velocity is an important rate of change, it is certainly not the only rate of change that you will encounter. Any time something changes, you can determine how quickly it is changing and express that as a rate of change. For example, you could measure how much money you put in your savings account and express that as a rate of change, too. If you save $300 each month, then the rate of change of money in your savings account is $300/month.

Positive vs Negative Rates of Change

Now that you know what a rate of change is, let's talk about what it means for a rate of change to be positive or negative. To get an idea about what this means, stand up and walk to the other side of the room. Assume that your starting point was at a position of zero. Then, as you walk, your position keeps increasing. Remember that the rate of change of your position tells you how fast you are walking - your velocity. So, in this case, you will have a positive rate of change, or a positive velocity.

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