# Day 12: Inventing Average Velocity

*College-Prep Physics:* We had a great discussion/debate about the meaning of average velocity today. Rather than give students the definition, I simply asked them to determine the average velocity for the following position-time graph (thanks Kelly O’Shea):

Students generated 8 different possible ways to compute the average velocity and I wrote them on the board (see top pic):

- The average of the magnitudes of the non-zero slopes.
- The average of the non-zero slopes.
- The average of the magnitudes of all slopes.
- The average of all the slopes.
- A time-weighted average of all the magnitudes of all slopes.
- A time-weighted average of all the slopes.
- Total distance divided by time.
- Total displacement divided by time.

Then we calculated each one and saw we got mostly different answers.

Students: “Which one’s right?”

Me: “So, how do we find the velocity for part of the trip?”

Students: “It’s the slope of the position-time graph.”

Me: “So how about the whole trip?”

Students: “The slope from start to finish?”

Me: “Yep.”

Students: “That’s 6 m in 6 seconds, so 1 m/s north.”

Me: “Did any of your methods yield the same value?”

Students: “Methods 6 and 8.”

Me: “Can you see why?”

And so we discussed how those two methods and the “net slope” method of finding the average velocity are really all the same thing.

It was a really great discussion.

A copy of my handout (with Kelly’s graph) is here: WORKSHEET Interpreting Position Time Graphs 2015

##CVPM

*NGSS Science and Engineering Practice 6: Constructing Explanations and Designing Solutions*