### Five days of acceleration

Monday began with the acceleration of a RipStik from a velocity of zero meters per second to roughly 2.5 meters per second nine meters later.

 030 Constant Acceleration time (s) distance (m) time (s) velocity (m/s) acc (m/s²) 0 0 0.00 0.00 0.45 1.34 1 1.34 0.75 0.56 2.13 2 2.13 1.27 0.66 2.79 3 2.79 1.52 0.38 3.84 5 3.84 1.90 0.37 4.67 7 4.67 2.41 0.61 5.47 9 5.47 2.50 0.11

As I chose to do last term, I had three timers timing splits at one, two, three, five, seven, and nine meters.

I made two runs. The Desmos screenshot would be the basis of a handout for use on Wednesday.

Wednesday I began with the introduction of the concept of a slope and y-intercept for a quadratic. Again this term the class did not know that quadratics have slopes and intercepts. After developing out the full motion equation I noted that the above image shows only one leg of a parabola - hardly convincing of what the curve should do on the left side of the graph.

I then took the class outside to demonstrate the full parabolic shape of the curve.

I used preset marks at 3, 6, and 9 meters uphill towards the LRC. To time the vertex (apex) I put a midline on the sidewalk visible in the image above. I asked the timers to time that crossing while Chastity marked the crossing point with a piece of coral after I crossed the midline. The vertex remains problematic, but otherwise a parabolic curve arguably well fits the data. A vertext at 10 meters would fit better, but data is data. Using the equation (done in the field on Desmos) I could compare my acceleration on Wednesday with the two I obtained on Monday. The students had a handout of the equation from Monday to consult. I could also compare my initial velocity of 3.1 m/s to the 1.53 m/s linear velocity run on the Monday a week and half ago.

I led off lab with the dropping of a plastic and metal ball to demonstrate that the rate of fall is independent of weight. I used this to frame the work of the lab. Is the fall rate constant once it gets under way? Constant velocity? Or changing velocity? And if changing, is the rate of change constant? If the rate of change of velocity is constant, then that rate of change is a constant acceleration. Which we could call the acceleration of gravity.

Masabua holds the meter sticks for Jesse.

Mayson and Sheeron work on the two meter drop

Four and five meters from outside on a sunny day

Data from the laboratory along with the regression to determine g. Desmos makes this part of the laboratory run smoothly. The value of g is directly displayed.

On Friday, having already seen that once again some lab introductions betrayed confusion, I led with a restatement of the intent of the laboratory.

This allowed me to segue from data generates shapes on graphs and those shapes imply mathematical equations or models to shapes can directly lead to equations.

I had the class trace the arc of a tennis balls, six balls, six arcs to be precise.

I then added coordinates to three of the six and asked the students to form groups and work out what the equation was for one of the three arcs. The students chose their own groups and group size, the students also chose which graph to work on.

Praislyn, Jessie, Chastity, Caslyn, Patricia, Kiokalani discussing options

Monday I determined that only three groups had an equation that provided a useful starting place. for a class examination. Two of the groups, however, were spot on - they had equations of the correct form that well matched the data. There was no need to construct our way to a working equation, two were numerically correct. Both were derived from trial and error in Desmos. Given this, I went ahead and led the class through the logic of the equation and showed that the theoretically derived equation was equivalent to the two equations which were found by trial and error using Desmos. This activity still went well, and segues moderately well into the Wednesday banana leaf marble ramp.