RipStik Logistic Curve for algebra and trigonometry class

In chapter five, section five, of the Larson Algebra and Trigonometry text book the author introduces mathematical models. Summer provides a 90 minute period, which affords some space to experiment within.

In the past I had used the speed versus distance along a track for a 100 meter sprinter to demonstrate a logistic model, yet this remained abstract. I do not know why I had thought of it before, but I realized that if accelerated at a constant rate for a short distance and then held a constant speed, the velocity data should mimic that of a sprinter. A brief constant rise in velocity to a top end velocity.

This generates the "upper half" of a logistic curve. I went outside and used seven stopwatches in the hands of seven students to time at 100, 200, 400, 600, 800, 1200, and 1600 centimeters. Accuracy could have been improved by a single stopwatch held by me doing the timing, but that would distract me from the steady acceleration to cruise. The spacing was designed to capture the 400 centimeter acceleration I planned to do, followed by a long cruise phase.

Sidewalk marks were still in place from earlier physical science runs, I only added the 100 and 200 cm marks. I ensured the stopwatches were all in split mode this time, and had the students test their watches. Data was captured in a single run, the RipStik started from a standstill.


The first table developed suggested that something went wrong for the timer at 200 cm as the speed over the segment 100 to 200 cm was 244 cm/s, far faster that I was going at that point. I also apparently slowed down over the final 400 cm, that data point was also removed. That happened over the flat as I prepared to dismount. A small amount of board swizzle should offset that, plus running out past the 1600 mark.

time (s) speed (cm/s) logistic model
0 0 5
2.44 41 46
4.35 133 154
5.31 208 207
6.15 238 236
7.67 263 256

Graphing the data against a custom tweaked logistic equation produces the following graph.


I was surprised by the "S" shape. Sprinters only generate the "upper half" of the logistic. I suspect the lower half is potentially spurious and not necessarily real. That said, an instructor has to run with what nature and the students have produced, in this case a more characteristically logistic curve than I expected.

Taking the data to be valid, the slope of the curve is the acceleration. I did not share this with the class as the point was to generate a logistic model, not to analyze the meaning of the curve. That the slope changes indicates a varying acceleration. I suppose the only way to ascertain whether there is an initially low acceleration phase will be to run this again at some future time.

Popular posts from this blog

Box and whisker plots in Google Sheets

Traditional food dishes of Micronesia

Creating histograms with Google Sheets