Student Guide
Summary of Mathematical Relationships
The Physics LE simulations allow you to explore various physical behaviors, and determine how one physical quantity is related to another. By varying one quantity and observing how a second quantity responds, you can determine the mathematical relationship between the two quantities. Some of the more common mathematical relationships found in physics are given below. Use the information provided here to help you determine the mathematical relationship between two physical quantities. The simulation exercises may require you to record only two or three sets of values, however, you may wish to record additional sets of values to help confirm the mathematical relationship.
Direct Relationship
Mathematical Form: y = kx (k is a constant)
Description: y is proportional, or directly related, to x
Example: When we double the value of x, then y also doubles. When we triple the value of x, then y also triples. If we reduce x to half its value, then y is also reduced to half its value.
Inverse Relationship
Mathematical Form: y = k/x
Description: y is inversely proportional to x
Example: When we double the value of x, then y is reduced to half its value. When x is tripled, then y is reduced to 1/3 its value. If we reduce x to half its value, then y becomes two times larger.
Square Relationship
Mathematical Form: y = kx2
Description: y is proportional to x2
Example: When we double the value of x, then y becomes 4 times larger. When x is tripled, then y becomes 9 times larger. If we reduce x to half its value, then y is reduced to 1/4 its value.
Inverse Square Relationship
Mathematical Form: y = k/x2
Description: y is inversely proportional to x2
Example: When we double the value of x, then y becomes 4 times smaller. When x is tripled, then y becomes 9 times smaller. If we reduce x to half its value, then y becomes 4 times larger.
