After 4 days of acceleration lab, I finally was able to figure out how to get students to use their data to determine the equations of motion for an object moving with uniform acceleration.
Unfortunately, the explanation is not strictly speaking correct. excellent discussion is provided in our Arnold Arons classic, Teaching Introductory Physics.”
First, students, after recording positions and times, calculate the average velocity over each time interval.
The question is then what is the instantaneous velocity at the end of each time interval? just as we plotted the position versus time, now we plot the instantaneous velocity.
To do this I had students equation of the physics definition of average velocity to the mathematical definition of an average of two numbers. Unfortunately, this idea is conceptually incorrect, and is often used in introductory physics courses. To see why this explanation is not correct, try taking the average of three instantaneous velocities and seeing if you get the actual average velocity. What’s really going on here is a sleight of hand, and it works only because my object is subject to uniform acceleration. (parenthetical aside next year I will have students derive the equation of position versus time from the velocity equation by calculating the displacement as the area under the velocity graph.
I have no idea how to do it any better though, and I am reluctant to use the ticker-tape timers