Multiple Representations is the idea that a physical phenomena can be explored in many different ways. For example, there is the physical representation which models the system with figures and diagrams, such as a free body diagram. There is also the mathematical representation which uses the equation(s) governing the physics of the system. All of the representations can be used together to help us understand and quantify the physical phenomena.

 

Observe the different types of representations for this section below;

Physical Representations explain the features of the situation in a visual way, often with vector representations of physical quantities overlaid a simple diagram or picture of the situation.

Several Videos use FBD's and a problem statement to connect with 2nd Law. 

Warning: the notation used to identify forces that are canceling out is very similar to KC's notation for force pairs. A normal force and gravity can never be Newton's third law force pairs even if they are canceling each other out acting on an object.

Video 1

 

Video 2

 

Video 3

Mathematical Representation uses equation(s) to describe the situation.
 

Page 3 of this site does a wonderful job of showing many of the different representations.

Graphical Representation describes the situation through use of plots and graphs.

Since translating a FBD is all about using Newton's second law, it's section on the graphical representation is a great place to learn more.

Descriptive Representation is made up enitrely of words or annotations. Think about how you might explain the situation to someone else.

This can be thought of as a word problem. For example, “If Steve pushes a one kilogram box for twelve seconds, and it goes five feet, how hard did Steve push?” would be a descriptive representation of a problem where you would have to translate a FBD into Newton's second law.

 
Actual Phenomena could be thought of as doing the experiment. For example, if you're asked which of two runners, with different characteristics of their speeds, will win the race, one way to determine that would be to get two runners to run in the described way and see who wins.