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?”
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
NGSS Science and Engineering Practice 6: Constructing Explanations and Designing Solutions