8/26/09 Physics Class

In class today, after we got back various old homeworks, we looked at a constant velocity model. The model showed two cars, A and B, both traveling at a constant velocity. Our task was to find the equation of each of the cars. The trick was remembering that the slope of a line is not simply y over x. Although this worked for car A because it went through the origin, it did not work for car B.
Next we discussed the graph of the falling basketball. We all knew that the graph was not a straigt line. Instead, the graph formed a parabola or a quadratic. We all knew that the equation of a parabola is y equals x squared. Mr. Burk asked us how we could prove that. This led to a discussion of the meaning of directly proportional. If a line is directly proportional it is straight and it passes through the origin. We realized that if the y-axis of a graph was position(x) and the x-axis was time squared and a line on the graph was directly proportional, it meant that position was a function of time squared. So to prove that position was a function of time squared in our lab, we squared all the original numbers and made a new graph to see if it formed a straight line. And..... it worked! This method is called linearization.

After that we took another look at our original graph. We had already agreed that the original graph was not a straight line. But when we zoomed in on certain time intervals that consisted of only 4 or 5 points, we noticed that they seemed to form a straight line. Mr. Burk even used a ruler to show us that the points really did make a straight line. We did this with points at the beginning of the graph and points at the end of the graph. The difference was, that the points at the end had a steeper slope than the points at the beginning. We concluded that over a small time interval, the position seems to follow the constant velocity model. At a later time the slope is steeper because the average velocity is greater. This is called instantaneous velocity. Our next discussion was, how do you find instantaneous velocity? You find the average velocity over a "small enough" time interval. How small is "small enough"? - As small as possible. We used the double interval method to do this. To find the instantaneous velocity of a point, simply find the average velocity of the point before it and the point after it. That concluded today's class.

Tomorrow's scribe: Mary Elizabeth