# Unit 3 Activity 12 - Plotting & Analyzing Velocity/Speed Graphs

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Help your students learn to create and analyze velocity and speed graphs using this quick set of graphing problems! Field-tested with hundreds of students and years in the classroom, designed to get maximum results with minimum time invested for both student and teacher!

Building upon Activities 9-11, students should now be developing confidence in their ability to graph and calculate a basic slope. Now, students will be given the additional tasks of creating their own scale for plotted data and calculating the area ‘underneath’ their graph (using basic area formulas, not integration).

In each problem, students are required to:
- Determine an appropriate scale
- Plot points on a pre-drawn graph
- Create a line of best fit from the plotted points
- Use points on the line to determine the acceleration of the object in question
- Use a best-fit line (and the area contained within) to determine the displacement of the object in question

The first problems provide students ‘perfect data’ that (when properly plotted) will place all points on the best-fit line. In the second section, students are given ‘real-world data’ that will create variations in best-fit lines due to the added human element in drawing best-fit lines. The last section will require students to determine the data points for velocity/speed, creating a reinforcing loop about the relationship between speed, displacement and acceleration.

The problems direct students to indicate which points they use in determining their slope. Students must use points that fall on the best-fit line, and if they don’t, they must determine new points that fall on their line. This is the most common mistake students make in my experience, as they want to simply use data points (or plug numbers into a = v/t). Both of those mistaken methods are only awarded credit if they actually fall on a best-fit line as well, which leads to many points given away because students use a lazy and incorrect technique.

An easy way to help students adhere to proper technique is to require them to circle the two points they used on their graph. This results in much higher rates of proper slope application in determining the best-fit slopes.

Used in conjunction with the entire Unit 3 slate of activities, Activity 12 will give your students the tools they need to be successful when dealing with graphs!

Correlates with standards and questions on the New York State Regents Exam in Physics. Also aligns strongly with many other standardized test questions in linear motion (AP Physics 1/2, SAT II Physics).

Activities:
- Plot data for velocity and speed on a pre-drawn graph
- Use plotted data points to create a best-fit line using regular data points
- Use plotted data points to create a best-fit line using irregular data points
- Determine the slope of a best-fit line
- Use slope of a velocity vs. time graph to determine an object’s acceleration
- Determine the area ‘under the graph’ (between graph and x-axis)
- Use the area ‘under the graph’ to determine an object’s displacement
- Use v = d / t to determine data points to use in graph
- Use vf = vi + at to determine data points to use in graph

Contents:
- 14 problems (graphs)
- 65 tasks in total in questions
- 6 graphs with ‘perfect’ values
- 5 graphs with ‘real-world’ (slightly inconsistent) values
- 3 graphs with values students solve for themselves
- Detailed answer key with sample best-fit lines and Excel-generated ‘true’ best-fit lines
- Activity comes in PDF format, ensuring accurate reprints
- Equation and Reference Sheet provided
Total Pages
14 pages
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