Constant Velocity Motion Lab (31/25) [APC Only]

This picture will not be completely sensical if you haven't had calculus, and don't worry about that. I include it here because some have, and because it shows you one of the things we'll be learning. Don't stress on this, we'll spend a lot of time on it.

 

As was seen before, calculating the slope at every point in the data set produced error because each point had measurement error. It would be much better if there was a way to get the slope of every point along the entire best fit equation to generate a new equation. This would be equivalent of getting a tangent line at every single place and getting its slope.

 

Accomplishing this was the reason that Isaac Newton and Gottfried Liebniz invented calculus. The act of getting a new function that gives us the slope of another function at every single place in its domain is called taking the derivative. The rules for derivatives of polynomials are in white on the left side. As can be seen, taking the derivative of our position graph gives us our velocity graph

Done