Calculus description of Constant Acceleration Lab
At the top we see the two equations of the (t,y) graph from the Angry Bird lab and the (t,v) graph from the same lab. We walked through in class what the meaning of the two equations are. It may be noted that the (t,v) equation does not agree with the values for acceleration and original velocity that are in the (t,y) equation. This is because of our method of plotting average velocities to make the (t,v) graph. It introduces considerable error into the measurements as each calculation is based on two data points, rather than all 25+. The techniques of differential calculus can be used to generate a (t,v) graph that represents the original best-fit parabola. The math required to accomplish this is on the board in this slide. Note that it gives a new (t,v) equation that's slightly different than the one from the graph. This new equation is more accurate because it uses all of the original data.
Calculus description of Constant Acceleration Lab
At the top we see the two equations of the (t,y) graph from the Angry Bird lab and the (t,v) graph from the same lab. We walked through in class what the meaning of the two equations are. It may be noted that the (t,v) equation does not agree with the values for acceleration and original velocity that are in the (t,y) equation. This is because of our method of plotting average velocities to make the (t,v) graph. It introduces considerable error into the measurements as each calculation is based on two data points, rather than all 25+. The techniques of differential calculus can be used to generate a (t,v) graph that represents the original best-fit parabola. The math required to accomplish this is on the board in this slide. Note that it gives a new (t,v) equation that's slightly different than the one from the graph. This new equation is more accurate because it uses all of the original data.