This 3-part interactive tutorial uses multiple graphs to explore the relationship between the motion of an object and the shape of its position vs. time 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.
This item is part of The Physics Classroom, a comprehensive set of tutorials and multimedia resources for high school physics students.
See Related Materials for a research-based diagnostic tool to identify and address misconceptions related to concepts of 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.
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.
Common Core State Standards for Mathematics Alignments
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.
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.
%0 Electronic Source %A Henderson, Tom %D December 15, 2007 %T The Physics Classroom: Describing Motion with Position vs. Time Graphs %V 2013 %N 18 May 2013 %8 December 15, 2007 %9 text/html %U http://www.physicsclassroom.com/Class/1DKin/U1L3a.cfm
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