This 3-part tutorial, developed for high school physics students, uses multiple graphs to study the relationship between the motion of an object and the shape of its p-t graph. Special attention is given to the meaning of the graph's shape to help beginners differentiate constant velocity from accelerated motion. The slope equation is illustrated in an interactive format allowing for learner self-evaluation. The tutorial is designed in a manner to help dispel common student misconceptions about the meaning of position. See Related Materials for an accompanying lab by the same author.

This item is part of The Physics Classroom, a comprehensive set of tutorials and multimedia resources for high school physics students.

Editor's Note:Education research indicates that students have difficulty relating real-world motion to a graph. In particular, many incorrectly plot position graphs as the path of an object. See Related Materials for a free research-based diagnostic tool to probe misconceptions related to motion and force.

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.

9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

9. The Mathematical World

9B. Symbolic Relationships

6-8: 9B/M3. Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease, increase or decrease in steps, or do something different from any of these.

9-12: 9B/H4. Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.

9C. Shapes

6-8: 9C/M4. The graphic display of numbers may help to show patterns such as trends, varying rates of change, gaps, or clusters that are useful when making predictions about the phenomena being graphed.

Next Generation Science Standards

Crosscutting Concepts (K-12)

Patterns (K-12)

Graphs and charts can be used to identify patterns in data. (6-8)

Patterns can be used to identify cause and effect relationships. (6-8)

NGSS Science and Engineering Practices (K-12)

Using Mathematics and Computational Thinking (5-12)

Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)

Use mathematical representations of phenomena to describe explanations. (9-12)

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.2 Reason abstractly and quantitatively.

Expressions and Equations (6-8)

Understand the connections between proportional relationships,
lines, and linear equations. (8)

8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Functions (8)

Use functions to model relationships between quantities. (8)

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.^{?}

Common Core State Reading Standards for Literacy in Science and Technical Subjects 6—12

Craft and Structure (6-12)

RST.9-10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9—10 texts and topics.

RST.9-10.5 Analyze the structure of the relationships among concepts in a text, including relationships among key terms (e.g., force, friction, reaction force, energy).

Range of Reading and Level of Text Complexity (6-12)

RST.9-10.10 By the end of grade 10, read and comprehend science/technical texts in the grades 9—10 text complexity band independently and proficiently.

This resource is part of a Physics Front Topical Unit.

Topic: Kinematics: The Physics of Motion Unit Title: Graphing

Excellent self-guided tutorial promotes understanding of "position" as a physics concept. Contains multiple graphs, animations, and interactive opportunities for students to test their comprehension.

<a href="http://www.thephysicsfront.org/items/detail.cfm?ID=3312">Henderson, Tom. The Physics Classroom: Describing Motion with Position vs. Time Graphs. December 15, 2007.</a>

Henderson, T. (2007, December 15). The Physics Classroom: Describing Motion with Position vs. Time Graphs. Retrieved June 25, 2017, from http://www.physicsclassroom.com/Class/1DKin/U1L3a.cfm

Henderson, Tom. The Physics Classroom: Describing Motion with Position vs. Time Graphs. December 15, 2007. http://www.physicsclassroom.com/Class/1DKin/U1L3a.cfm (accessed 25 June 2017).

Henderson, Tom. The Physics Classroom: Describing Motion with Position vs. Time Graphs. 1996. 15 Dec. 2007. 25 June 2017 <http://www.physicsclassroom.com/Class/1DKin/U1L3a.cfm>.

@misc{
Author = "Tom Henderson",
Title = {The Physics Classroom: Describing Motion with Position vs. Time Graphs},
Volume = {2017},
Number = {25 June 2017},
Month = {December 15, 2007},
Year = {1996}
}

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An annotated list of documented student misconceptions related to concepts of position, velocity, and acceleration. Contains probative questions to elicit and address the misconceptions.