# Day 57: Mistake Made in Haste

Yesterday I was so enamored with a group’s creation of the average velocity step graph that I neglected to check that group’s math.

Turns out they calculated the average velocity using the total distance rather than the interval distance. In other words, they simply took the distance column and divided by the time column. (Just goes to show how fragile students’ knowledge is, and how subtlety and nuance is difficult for students to grasp.)

Sooooo I graphed their data again, this time using steps that start at t=0 (in black above). This meant the steps overlapped and it was hard for me to see the “best fit line” in this case (also in black) though this time there is no intercept.

In red, I calculated and graphed the interval average velocity that I thought they had done originally. Yikes! The average velocity is all over the place. Small timing errors seem to have a much bigger effect for the interval velocities.

I still like the activity, but I don’t want to make it more complicated than necessary, especially with errors in the interval velocities.

Have everyone do it their own way first and repeat having everyone use time as independent variable? Skip the velocity graphing altogether (my original intention, until I saw the students’ step graph)?

Thanks for your help!

Frank, I had the same issue this year. One group had a great solution. First, they found the quadratic trendline to x-t using linearization. But since they still wanted to know the velocity trend (without dealing with the huge amounts of error), they then calculated interval-velocities using points on the x-t trendline instead of x-t data points. Beautiful linear graph, and CA emerges nicely…