# 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):

1. The average of the magnitudes of the non-zero slopes.
2. The average of the non-zero slopes.
3. The average of the magnitudes of all slopes.
4. The average of all the slopes.
5. A time-weighted average of all the magnitudes of all slopes.
6. A time-weighted average of all the slopes.
7. Total distance divided by time.
8. 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

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