Welcome your students to class and remind them about the Betabox Field Trip that they recently participated in. Summarize the Field Trip of when they built their own LEGO-like drones and flew them. Then, they launched the drones vertically to time how quickly they would rise to a given height. Finally, they attempted to smash their drones into one another.
Inform your students that in today’s class, they will be further analyzing the time trials portion of the Field Trip and will use the data they collected to learn about average velocity.
Pass out some blank paper and instruct students to gather their data sheets from the Field Trip. Since students worked in groups for collecting the data, ask them to reform in those groups.
Alternatively, you could take a few minutes for those groups to share the data they collected on their group data sheet with all group members so each student has the data they need to complete the activity.
2. Finding the average time
3 – 7 mins
Using calculators, instruct students to calculate the average of the three trials to find the average time that the drone took to reach the designated height.
If some groups don’t have data because they did not complete their drone in time, provide sample data or ask them to share data from another group.
3. Introduce displacement vs distance
5 – 7 mins
Say: Let’s think back to the Field Trip to the part when you were trying to get the drones to fly up to that balloon (or ceiling). Who was able to do that? Who was able to get it up really straight? Whose drone took a more meandering upward path?
Draw a diagram on your whiteboard of the drone and the balloon. Have students explain to you the true path that their drones took. Some will have flown straight up (linear) while others may have zigzagged or swirled upwards.
Use these diagrams as a jumping-off point to introduce the difference between displacement and distance traveled.
The balloon was 10m up in the sky, so in the up-and-down vertical (the y-axis) direction your drone went how high? (Answer = 10m)
Right, but what about those zigzags? If you added up that whole path would it still be a total travel distance of 10m?
No, it would be more. We call the up-and-down vertical amount displacement in physics and the total zigzag path distance traveled. This is an important difference! Being able to talk about these different paths is key so that we’re on the same page when discussing the same topic.
Write the equation for displacement on the board where xf is final distance and xi is initial distance:
4. Introduce vectors
This displacement term is a vector, which is a special type of number that includes both an amount and a direction. We call a number that just has an amount a scalar and the physics word for an amount is magnitude.
So, in the drone situation we could use the ground as our point of reference and we could label the balloon at +10m (+ because it went higher above the ground). We’d say that our drone displaced 10m in our trail, even if the distance traveled was longer.
One neat thing about this is we could set the reference frame however we’d like. As long as all the objects are relative to the same things, we can establish different set points. We could choose to set the balloon at 0m and the ground at -10m, it is up to us! The difference should still be the same. Usually, we like to label the diagrams we make with the easiest numbers we can. That is partially out of laziness, but more so out of ease of explaining our model/work. Doing these as simply as we can does help us avoid mistakes.
Note!! If you are talking about displacement, you need to have the + or – in front of your distance term, that is what turns it into displacement. Also, try not to get confused that distance in physics is the magnitude (or scalar) portion of the displacement. Distance traveled is what a physics person would say if they were trying to talk about the zigzag path.
Pause for questions.
Here is something to think about: what if we change the amount of time that we are including in our trial? What if we added the path down into this diagram as well? What would the displacement be?
It would be 0 in the y-direction. If you are being technical you could have some x-direction displacement if your drone didn’t land in the same place. For example, if your drone landed 5m from where it launched, the x-displacement would be 5.
5. Calculating average velocity
Ask: If your drone traveled 10m upwards in 5 seconds, how fast was it going? That is what we can figure out next.
Explain: The equation we are going to use to figure this out is the average velocity equation.
But, what is average velocity? It’s the change in position divided by the time of travel. Not time travel, time of travel.
When have you seen any equations like that before?
A: Rise over run with slopes
Yeah that is right, slopes. Velocity is somewhat like a slope. Just as slopes are about the rate at which the height of a line is changing, velocity is the rate an object’s height could be changing.
Introduce v = d / t
Everyone, take a moment to review the equation on the screen and use it to get the average velocity of your drones during the Field Trip.
Walk around the room and help students input the correct numbers. Note that the average time they calculated would be equal to t2 – t1, as t1 = 0.
And when you write your answer, make it AveV = +2m/s and put a box around it. In engineering school they like you to put boxes around it. Remember units!
6. Wrap Up
Pause to see if the group has questions.
Have students turn in their work papers.
Ask one of the students to summarize what they learned in the class today.
If time remains, ask other students to further summarize other things that they may have learned during the Field Trip.