One of the most difficult things for students to master during physics is graphs of position-time and velocity-time. This activity is an introductory exploration that starts from the simplest graph which is of a person standing still and moves up through the more complicated graphs with several different motions and various types of accelerated motion.

This helps the students really construct an understanding of each of these graphs individually and also construct an understanding of how these two graphs are related to each other.

The goal of this activity (which takes several days depending on the level of the students and their mathematical skills) are:

Describe the motion represented by a position-time graph.
Sketch a velocity-time graph to scale given a position-time graph.
Describe the motion represented by a velocity-time graph.
Sketch a position-time graph to scale given a velocity-time graph.

One of the most important aspects of this lesson is to allow students time to develop their own mental model of the graphs with just encouragement but not give away answers to the activity. Also encourage students to take turns in their lab group so everyone gets a chance to be the walker. The student who is walking, if they are looking at the live plot of their motion can gain a great understanding just by linking what they are doing with the line on the screen.

I have attached a copy of the instructions I give to my students during this activity.

Step 1: Why Make Predictions?

One of the most important things for students to do during this activity is to individually think about what graph they think will be produced by a certain action, and record what they are thinking.

I ask students to:

individually sketch their graph without consulting others
once their lab group has all made individual predictions, discuss their predictions as a group
if they choose to, students can change their prediction
all predictions have to include a reason why things happen the way they do

By having students do that, after they have completed the activity, they can look back at what they have done and reconcile their thinking to what actually happened.

Step 2: Introducing Students to Equipment

There are many brands of probeware that can be used successfully in classrooms. This is usually one of the first uses of the probes and software in my class so I spend a little time just introducing the students to the system. For this activity the functions that are important to model for the students include:

how to connect the equipment
how to save data
how to autoscale the axes of the graph
how to zoom in and out of the graph
how to read the coordinates of a datapoint off of a graph
how to use the slope tool to identify the slope at a specific point on the graph

I keep this introduction short so that students know these functions are present and if they realize they might want to use them they will click around or ask if they cannot find a function.

Then I give the students time to explore and discover the wonders of motion graphs!