Day four acceleration and the ½

The graph at the top left was pre-existing from earlier in the week - this week the cleaning crew left the board untouched. As the only class using the white board, the notes were able to build up over the course of the week. This term more care was taken to include the tables for each graph.

Starting with last week's constant linear motion, a time versus distance table and graph was produced for a velocity of two. The units were omitted today. The a time versus velocity table and graph was produced for the constant velocity of two (center top). On this graph the distance was shown to be the area under the velocity line. This was followed by a time versus velocity table and graph for a steadily rising velocity (center bottom). Then the distance was calculated as the area under the velocity line. Now, however, the shape under the line is a triangle, not a rectangle. The ½ now appears in the distance calculation from the area of a triangle: one half the base times the height.

Graphing the distances one arrives at a parabola. While this approach has mathematical issues, the approach avoids using calculus to make a plausible argument as to where the ½ comes in from. 

Then, for the sake of completeness, the integral calculus approach was done on the board without significant explanation.

The second topic tackled was the nature of the slope of a quadratic which can be seen center above. This portion of the lecture notes the apparent important attached to calculating a slope of a linear equation in mathematics classes and then the radio silence as to whether a quadratic equation even has a slope. 

The intent is to keep this math heavy lecture as short as is reasonably possible - this is heavy going. The material wrapped at 38 minutes.