In physics modeling instruction, the constant velocity particle model begins with a paradigm investigation of the motion of constant-speed buggies. This summer, I reprogrammed the Scribbler 2 Robot from Parallax Corporation to be a physics apparatus , and this was my first chance to use them. (I intend the robot project itself to be the subject of a future blog post.) For the robot lab, I programmed the robots to have speeds from 10cm/s to 18.5cm/s, but all to go 150cm before stopping.
When students did the lab, I got a variety of responses. Some groups graphed distance on the y-axis, and others on the x-axis. Some groups used inches, others used cm or feet. One group even did a conversion to km/h.
Groups made a variety of mistakes constructing data tables, setting not-so-even scales for their axes, etc. This collection of responses and mistakes provided a fertile ground for discussion of some important issues, as described well elsewhere (John Burk at Quantum Progress: Buggy Lab, mid teaching analysis and Buggy Lab day 2, first board meeting). Almost all students at this level measure and graph distance vs. time at this point, so the concepts of position and velocity are introduced in the next lab.
When we completed the post-lab discussion of the above issues, more or less as I have done it for years with the buggy lab, I then asked the students to rank the robots from slowest to fastest and to set them on the starting line in that order. This required conversions to a consistent set of units in order to make the comparison, which of course I requested be well-documented on their whiteboards. When they were done, we were able to test their prediction experimentally:
In previous years, I’ve asked students to similarly rank their constant speed buggies, but the buggies do not tend to run in a straight line nor maintain a perfectly constant speed. Their speeds can only be changed by replacing one battery with a metal plug, and slow down significantly as the batteries discharge. And the student’s measuring and graphing abilities typically were not up to the task of distinguishing among members of the one-battery and two-battery clumps of speeds. Experimental verification of a buggy speed ranking was never convincing, so I stopped doing it.
Thinking it would be an easy task, I followed up by asking the whole class to show all five robots on a single graph at the board in front of the room. First, they had to discuss and decide on a standard, i.e. whether to put distance or time on the x-axis. Then they started laboriously plotting individual points. After some prompting from me, they realized they could much more quickly graph the correct “shape,” without numbers. This was an important step, as it required viewing and interpreting the graph as a whole rather than just mechanically plotting points.
They pretty quickly figured that all the lines should start at zero, and the lines representing the faster robots should “be on top” because they “traveled farther in the same time,” resulting in the graph on the left, below. It took a question from me and several minutes of discussion to produce the correct graph at right showing the robots all traveled the same distance. Not such an easy task after all.
Once again, thinking I was posing a simple question to sum up the activity, I asked the students how to tell which robot was faster. When I got back several different answers, including that the one with the longest line was slowest, I had to ask them what it would look like if they all traveled for the same time, rather than the same distance. Several minutes of discussion later, they produced the graph below.
Only after producing and discussing the counter-example were they all ready to conclude that they should look at the slope to tell the fastest robot, although I was certain some still harbored the notion that the line that was on top would be the fastest robot, a misconception that would have to wait for the introduction of position to dispel. Once again, not so easy after all. I emphasized that interpreting the shape of a distance vs. time graph, without numbers, was important enough to be one of the standards their work would be graded on, and made sure that at least one student could explain to the class how to tell which line had a greater slope, just by visual inspection.
Initial emotional reaction to the robots was just that they were slow. There are ways to make them faster, and I had anticipated this problem, but development of the programming tools left me no time this summer to further pursue the speed issue. From a teaching perspective, I was very pleased because the post lab discussion was much richer and more spontaneous than previous years’ discussions with the buggy lab. Just the simple ability to program the robots with a range of clearly distinct speeds was a productive supplement to the traditional buggy lab. In subsequent exercises, I noticed the students taking greater care to properly locate the endpoints of their lines in position and time.