This tutorial explains how to read, construct, and interpret three basic kinematic graphs: Position vs. Time, Velocity vs. Time, and Acceleration vs. Time. It includes animated examples, links to five worksheets, and related problems for student exploration. This item is part of an online textbook in introductory physics.

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acceleration, acceleration vs. time graph, average acceleration, displacement, graphing motion, instantaneous acceleration, kinematics, motion graphs, position vs. time graph, velocity, velocity vs. time graph

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October 23, 2006
by Caroline Hall

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.

Next Generation Science Standards

Crosscutting Concepts (K-12)

Patterns (K-12)

Graphs and charts can be used to identify patterns in data. (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

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.

F-IF.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.

F-IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

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

F-LE.1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

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.

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

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

RST.11-12.10 By the end of grade 12, read and comprehend science/technical texts in the grades 11—CCR text complexity band independently and proficiently.

%0 Electronic Source %A Elert, Glenn %D June 27, 2007 %T The Physics Hypertextbook: Graphs of Motion %V 2015 %N 30 July 2015 %8 June 27, 2007 %9 text/html %U http://physics.info/motion-graphs/

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