Summary and Main Ideas

Summary

Graphical Analysis of One-Dimensional Motion

• Graphs of motion can be used to analyze motion.
• Graphical solutions yield identical solutions to mathematical methods for deriving motion equations.
• The slope of a graph of displacement \(x\) vs. time \(t\) is velocity \(v\).
• The slope of a graph of velocity \(v\) vs. time \(t\) graph is acceleration \(a\).
• Average velocity, instantaneous velocity, and acceleration can all be obtained by analyzing graphs.

Glossary

Independent variable

the variable that the dependent variable is measured with respect to; usually plotted along the x-axis

Dependent variable

the variable that is being measured; usually plotted along the y-axis

Slope

the difference in y-value (the rise) divided by the difference in x-value (the run) of two points on a straight line

y-intercept

the y-value when x = 0, or when the graph crosses the y-axis