Acceleration day two

On Wednesday the board still had the predicted parabolic curve from classwork done on Monday. 

With the graph on the right still on the whiteboard, I held the Tripltek up to the board to show that the predicted shape had come true.


This led naturally to a review of the equation d₁~½at₁² from Monday and d = vt from the prior Monday and the illustration of the parallel equations in algebra. I then asked whether the parabola had a slope. The class was silent. One student ventured to answer that no, the parabola had no slope. I then explained to the class that the parabola had a slope and they should demand a refund for any money they spent on learning mathematics in math classes. Math classes cannot teach one to think mathematically, to possess mathematical insight. That no one realized a parabola has a slope does not mean math classes should teach this specific fact. No. This is not a failure of coverage of some specific fact. This is an indictment of what mathematics education tends to produce: students who either dislike mathematics, believe they are no good at math, or both. 

I then covered the slope of the quadratic equation explaining that the formula came from calculus, that, no, you will not be tested on this, and, yes, it is alright to see mathematics that you cannot yet yourself do. The equation would lead to the other half of the 


This term I measured off distances of 3, 6, 9, and 10 meters. I passed out a half dozen stopwatches. The more the merrier and the more likely someone would get solid data. 

Desmos

I actually plotted two sets of data, but the second set produced a smoother curve. The 2.81 m/s v₀ was well above the 1.6 m/s and -1.56 m/s runs of a week ago Monday. My turn was reportedly exactly at 10 meters. The acceleration above is -0.40 m/s²  a value in line with prior accelerations. The negative sign is indicative of the vertex being a global maximum value for the function. If anything, there was more curvature apparent in this data that was seen spring 2022. 


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