Acceleration day two
The subtheme of running with three meter lap distances was carried over into today with surprisingly good results. Prior to class I marked off three meter segments on the uphill into the LRC. I did not, as I have in the past, mark a ten or eleven meter mark.
Zero was in the traditional location on the left.
No marks were made at ten and eleven meters, only a new line up at 12 meters. Historically, no run has attained twelve meters.
The class started in A101 where I laid out the table seen on the left. A test run at 11:45 AM had failed producing only five times. I had missed two timing marks. The right side was done upon return from the field. The class got out to 12 meter marks at 12:09 and was back in the room by around 12:25.
Knowing that the timing is complex, this term I kept a stopwatch and took times myself. I also distributed timers so others could practice timing my run. The day was exceptionally set and rainy. My Hoka Challenger 7 shoes proved too slippery when wet and I was unable to bring the board up to speed - my feet kept sliding on the deck.
New to this term, on Monday I had shown that two mathematical models fit the data equally well.
On Monday the exponential was a better fit. The shape on Wednesday, however, argues that the parabolic model is the correct mathematical model. In class I could sense that this argument was a long reach for the students. They are not accustomed to thinking of equations as having shapes in the generic sense, in the sense of a Platonic ideal, in the sense of a family of curves. Everything is simply equally mysterious and baffling for the students. I could only argue that the green line doesn't work for this data, but the parabolic shape did.
The initial speed of 2.35 m/s appears to be lower than prior terms, probably a result of the wet conditions. Spring 2023 saw an inbound velocity of 2.83m/s/ The board is also aging and the wheels are wearing down, the bearings are ungreased. Perhaps someday a new board.
The deceleration of -0.30 m/s² is also low. Spring 2023 the deceleration was -0.45 m/s², in the ball park of -0.5 m/s².
The exponential equation that worked so well on Monday failed to model the behavior of the system on Wednesday. The parabola was the better model.
One of the wrap up calcuations I made was to show that near the vertex my velocity was close to zero. Using the slope equation that v = at + v₀ and the vertex coordinate (7.8, 9.2) I calculated -0.30*7.8+2.35 = 0.01. Very close to zero velocity. The presages a week four exercise from spring 2023.
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