This introductory tutorial provides examples and visualizations for beginners in the fundamentals of graphing Velocity vs. Time and Position vs. Time. Physical quantities are related to graphical features, such as the relationship between slope and velocity. Images and Flash animations are used to present the material, along with examples that demonstrate problem-solving using formulas relating to displacement and constant velocity.

Editor's Note:We recommend this tutorial as review for students who have already been exposed to P/T and V/T graphing functions. It could also serve as remediation for students still struggling with the concepts post-instruction.

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

9. The Mathematical World

9B. Symbolic Relationships

6-8: 9B/M2. Rates of change can be computed from differences in magnitudes and vice versa.

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.

Common Core State Standards for Mathematics Alignments

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.^{?}

F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Linear, Quadratic, and Exponential Models^{?} (9-12)

F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

F-LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

<a href="http://www.thephysicsfront.org/items/detail.cfm?ID=1156">Dicker, Jason, and Ed Love. Physics for Physical Sciences: Graphing Motion. 2002.</a>

J. Dicker and E. Love, Physics for Physical Sciences: Graphing Motion, (2002), <http://www.launc.tased.edu.au/online/sciences/PhysSci/done/kinetics/grap_eqn/Grmotion.htm>.

Dicker, J., & Love, E. (2002). Physics for Physical Sciences: Graphing Motion. Retrieved November 28, 2015, from http://www.launc.tased.edu.au/online/sciences/PhysSci/done/kinetics/grap_eqn/Grmotion.htm

Dicker, Jason, and Ed Love. Physics for Physical Sciences: Graphing Motion. 2002. http://www.launc.tased.edu.au/online/sciences/PhysSci/done/kinetics/grap_eqn/Grmotion.htm (accessed 28 November 2015).

@misc{
Author = "Jason Dicker and Ed Love",
Title = {Physics for Physical Sciences: Graphing Motion},
Volume = {2015},
Number = {28 November 2015},
Year = {2002}
}

%A Jason Dicker %A Ed Love %T Physics for Physical Sciences: Graphing Motion %D 2002 %U http://www.launc.tased.edu.au/online/sciences/PhysSci/done/kinetics/grap_eqn/Grmotion.htm %O text/html

%0 Electronic Source %A Dicker, Jason %A Love, Ed %D 2002 %T Physics for Physical Sciences: Graphing Motion %V 2015 %N 28 November 2015 %9 text/html %U http://www.launc.tased.edu.au/online/sciences/PhysSci/done/kinetics/grap_eqn/Grmotion.htm

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