
"Physics is Fun" Feimer's Physics Page 
Links to Current Lessons __________________________ Physics Topics
Introduction to Math
and Measurement
Displaying (and Processing) Data
Making Tables and Graphs
with Excel Spreadsheet
Study
of Planetary Motion and the Law of Universal Gravity
Study
of Momentum and the Conservation of Momentum
Study of Work,
Power, and Energy
Study of Waves, Energy, Light, and Sound __________________________ Astronomy Topics 
Displaying Data Below you will find information about three types of relationships commonly found in the study of science including physics. Before you read and study this material, you may want to review the information about plotting points on graphs and displaying and interpreting data on graphs. The link below will take you to this information. Direct Variation: Direct Proportionality / Linear Relationship / y a x Inverse Variation: Inverse Proportionality / y a 1/x Parabolic Relationship: y a x^2 . 
Direct Variation: Also known as a linear relationship,
it involves a relationship between two variables defined or described by
a straight line. As the independent variable is increased the dependent
variable increases proportionally (and visavis). The variables' values
are said to be proportional to one another. The "generic" Equation defining
this type of relationship or function is y = mx + b. The variable
value m is equal to the slope of the line. The variable value b is the
value of the y intercept, where the line graph crosses the y axis.
Below is an example of a positiontime data for a situation
where an object is moving along with a constant velocity. Examine the data
table and then the graph of the data. A scatter plot is being used to visualize
the data in graphical form. You may connect the dots plotted to see the
continuous function nature of the relationship and to do interpolation.
(Look up scatter plot and interpolation, if you are unfamiliar with the
concepts.)

Inverse Variation: Also known as a hyperbolic
relationship, it involves a relationship between two variables defined
or described by a hyperbola. As the independent variable is increased the
dependent variable does the opposite. The variables' values are said to
be inversely proportional to one another. The generic equation defining
this type of relationship or function is k = x y, where k is a numerical
constant that remains the same as x and y change respectively. In a single
graph of a a hyperbola the mathematical product of x and y remains a numerical
constant represented by the symbol k.
Below is an example of a volume vs pressure data set for
a situation where a specified volume of gas is being compressed by a defined
amount of increase in the pressure being applied to a moveable piston pressing
downwards on the gas. Examine the data table and then the graph of the
data. A scatter plot is being used to visualize the data in graphical form.
You may connect the dots plotted to see the continuous function nature
of the relationship and to do interpolation. (Look up scatter plot and
interpolation, if you are unfamiliar with the concepts.)

Parabolic Relationship: This type of relationship
involves two variables that have a more complex relationship than either
the linear or hyperbolic functions described above. The value of the dependent
variable is proportional to the square of the independent variable. The
generic equation defining this type of relationship or function is y
= kx^2, where k is a numerical constant that remains the same as x
and y change respectively.
Below is an example of a time vs position data set for a situation where an object is being accelerated over a short time interval. Examine the data table and then the graph of the data. A scatter plot is being used to visualize the data in graphical form. You may connect the dots plotted to see the continuous function nature of the relationship and to do interpolation. (Look up scatter plot and interpolation, if you are unfamiliar with the concepts.) Note: Look particularly at the second graph below
that represents the data table. It shows that there is indeed a direct
variation between the position of an object being accelerated and the time
over which it has been accelerated squared.
