3.1 Interpreting the Graph

The purpose of doing an experiment in science is to try to find out how nature behaves given certain constraints. In physics this often results in an attempt to try to find the relationship between two variables in a controlled experiment. Sometimes the trend of the data can be loosely determined by looking only at the raw data. The trend becomes more clear when one looks at the graph. In first year physics, most of the graphs we make will represent one of four basic relationships between the variables. These are 1) no relation 2) linear relationships 3) hyperbolic relationships and 4) parabolic relationships. There are many other types of mathematical relationships between variables. However, the vast majority of the experiments you do in an introductory physics course can be analyzed using some combination of the four above.

By examining the graph, you should be able to determine whether there is no relation, a linear relation, or possibly a hyperbolic or square relation between the variables. To more specifically describe the relationship between the variables in an experiment, you will be expected to develop an equation. An equation that describes the behavior of a physical system (or any other system for that matter) can be called a mathematical model. The information which follows will describe each of the basic types of relationships we tend to see in physics. It also describes the process for arriving at a mathematical model to more fully (and simply) describe the relationship between the variables and the behaviors of physical systems.