Unit 4.1 What is where?

By the end of this unit, students will be able to:

• Plot position-time and velocity-time data on a graph and interpret these data based on predictions and multiple trials.
• Explain the concepts of, and relationships between, position and velocity in order to predict how position & velocity will change with motion
• Use mathematical representations and proportionality to support claims regarding position, velocity, and time.

This unit provides an interactive introduction to making observations about position, velocity, and acceleration. It is a crucial building block toward our ultimate goal of understanding motions in Rube Goldberg Machines and similar obstacle-course challenges (this unit's motivating question).

Students will utilize many of the same quantitative skills they have been practicing all semester: interpreting direct/inverse proportionality; calculating and interpreting mean and standard deviation; inserting a best fit line to data and interpreting the results as physically meaningful from governing equations; using simple equations to make predictions and draw conclusions about data; and performing unit conversions.

The materials in this unit should take 105 min of class time, plus an additional 60-90 min if the extension activities are completed. Most of the lab exercises rely on small group work and are best suited to smaller classes or a lab meet-up outside of a traditional lecture room.

Teaching Materials:

Slides, Part 1 of 2 (use if you have motion detectors): U4.1 Part 1 of 2 - Yes motion sensors.pptx (PowerPoint 2007 (.pptx) 5MB Jul12 24)

Slides, Part 1 of 2 (use if you do not have motion detectors): U4.1 Part 1 of 2 - No motion sensors.pptx (PowerPoint 2007 (.pptx) 12MB Jul12 24)

Slides, Part 2 of 2 (extension lab/slides using tracker): Unit 4.1 Part 2 of 2 - Tracker v2 (PowerPoint 2007 (.pptx) 7.7MB Aug30 24)

Graphing Motion Activity (if using motion detectors only): Student file U4.1 Graphing Motion -Student Copy.docx (Microsoft Word 2007 (.docx) 376kB Jul11 24), Instructor file

U4.1 Graphing Motion - Instructor notes.docx -- educator-only file

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Graphing Motion Materials: Long meter stick (measure out 2-3 m along the floor) and one of the two following options:

• Motion sensors option: one motion sensor connected to a computer per lab group (or do this as a full-class interactive lecture demonstration). Motion detectors from Vernier work seamlessly, and this activity can be completed with just one motion detector per group and use the free version of Vernier Graphical Analysis/VGA (Vernier's GoDirect Motion Sensors connect via bluetooth to VGA and can work on a chromebook/ipad or laptop/desktop).
  • If you can use motion detectors, then we highly recommend that as it is a much better learning opportunity for students. Most physics labs and demonstration rooms have a collection of these probes that have been available for decades and cost <$100 per probe - if you are not working from within a physics department, then it's worth checking in to see if they have probes you can borrow.
• No motion sensors option: PhET Moving Man Simulation connected to a computer for each group.

Pirates Prefer Vectors activity: Pirate Map Handout U4.1 Pirate Map Handout.docx (Microsoft Word 2007 (.docx) 1.3MB Jul11 24), Activity Instructions U4.1 Pirates Prefer Vectors.docx (Microsoft Word 2007 (.docx) 263kB Jul11 24)

Graphing Motion Video Tracking Extension Activity:

• Optional handout: U4.1 Graphing Motion Extension.docx (Microsoft Word 2007 (.docx) 266kB Jul11 24)
• Materials: Phones for taking video and a way to move video files onto a computer; a sample of objects to record as they move, like balls, stomp rockets, toy cars; rulers/meter sticks, bits of wood for ramps.

Reflection Assignment: U4.1 Reflection.docx (Microsoft Word 2007 (.docx) 69kB Jul11 24)

Sample Student Reflections (this is Reflection 12): Reflection Examples Redacted.pdf (Acrobat (PDF) 1.8MB Jul8 24)

Scientist Spotlight Full Resource (In this unit: Konstantin Tsiolkovsky): Scientist Spotlight Slides (PowerPoint 2007 (.pptx) 4.6MB Jul8 24)

Pre-Class Assignment(s):

• Complete the next Scientist Spotlight. Spend a few minutes online doing additional research on Konstantin Tsiolkovsky and be prepared to share something surprising or interesting that you learned about him.

In Class, Part 1 (75 min): Position-Time and Velocity-Time graphs of motion

Introduction (15 min):

• Class discussion to introduce motion and complete the Scientist Spotlight using slide set.
  • Discuss Konstantin Tsiolkovsky (Scientist Spotlight). As always, the goal of these is to showcase an array of scientists in fields relevant to the topics of the day, some from long ago and others young and active today, together representing a diversity of people who have all overcome some challenge in pursuit of their scientific passion. More detail is in Teaching Notes and Tips.
• Introduce dimensions, space, coordinates, etc. and how position is determined within space. What is motion? A change in position.

Graphing Motion Lab/Activity (60 min):

Materials have been provided both for using motion detectors and for using the PhET moving man simulator. If you can use motion detectors, then we highly recommend that as it is a much better learning opportunity for the students.

• Complete Graphing Motion Lab. In this lab, students create position-time and velocity-time graphs of their motion. Students are asked to make predictions and discuss the results of walking quickly/slowly, standing still, walking backwards/forwards, walking in front of the origin/behind the origin, walk to match certain position-time and velocity-time curves and more. Once again, students are revisiting all the same quantitative skills that they have been practicing since Unit 2. By now, the students should be pretty good at the math side of these skills, but making and interpreting the graphs physically will still likely be a challenge.
• Press students to challenge themselves with some tricky questions as well! Remember to remind them to have a growth mindset that we started talking about way back in Unit 1.1 of this course! Challenge questions ask students to predict how you'd walk to produce more complicated position-time plots (and then to try it out with the motion detectors!), and to identify which velocity v. time graph(s) show motion to the left (negative direction) and slowing down?
• Introduce acceleration as velocity that is changing over time. We'll return to acceleration when we study forces next.

In Class, Part 2 (30 min): Pirates Prefer Vectors, yarr!

• (15 min): Pirates prefer vectors, yarrr! In this activity, students complete a Pirate Treasure Hunt (there are two options provided, one can be completed seated at desks, the other involves walking around): students must find the location of a hidden treasure by following directions with and without vector information (ex: Walk 10 yarrrds, then walk 5 yarrrds, then walk 6 yarrrds vs. walk 10 yarrrds east, then walk 5 yarrrds north, then walk 6 yarrrds northwest).
• (15 min): Guided discussion to recap, review, and build on the Graphing Motion Lab(s) completed earlier in the unit. Students will be incorporating these skills and ideas into their end-of-unit Rube Goldberg engineering exercise (Unit 4.4).
  • Think-Pair-Share: Draw velocity vectors representing: Walking slowly away from the origin (to the right); Walking rapidly toward the origin (to the left). Compare these vectors to the corresponding position-time and velocity-graphs. How are they similar? How are they different?

In Class, Part 3: Video Tracking Extension Lab (60-90+ min):

If time does not allow, this level-up lab can be skipped without loss of continuity to the rest of the course. Though tracking the motion of objects with the software might seem tedious, it makes tracking their position, determining velocity, and determining acceleration substantially easier! Note: Institutions that have a license to Vernier Graphical Analysis Pro or Vernier's Logger Pro can complete this exercise in those programs as well.

• (60-90+ min): Tracking Motion with Tracker. In this lab, students use tracking software to create a video of an object's motion and analyze it using an online tracker app. Instructions for using Tracker are included in the activity slides file - it is a straightforward and user-friendly website/app that can be picked up fairly quickly.  Outline of this Lab:
  • Students first choose their objects and design their simple motion (e.g. let a ball roll down a ramp then along the table; or pass a basketball to a partner) then set up to film their object in motion (2D motion)
  • After having designed and watched the object in motion, students should predict how the position, velocity, and acceleration will change during the object's travel path
  • Students upload their video to the tracking software and then conduct the video analysis to collect motion data (position, velocity, acceleration). The software produces tables of x position, y position, x velocity, y velocity, x acceleration, y acceleration, and far more. The columns of data of interest can be directly copied and pasted into a spreadsheet so that students can use a computer to quickly make graphs of each direction of position, velocity, and acceleration vs time in order to test their initial prediction.
  • Regardless of the outcome (correct or incorrect prediction), students should take some time to analyze and interpret their graphs. Students are strongly recommended to sketch a representation of the graphs in their notebooks and annotate them - here students can more easily overlay different datasets (e.g. x position and x velocity) on a single graph to interpret relationships between these two vectors.
• Now that we have conducted our own motion experiments and analyzed our own data, let's examine
  • how to interpret graphs of position vs time, velocity vs time, and acceleration vs time within the context of coordinates
  • the relationships between position and velocity, and velocity and acceleration
• Think-pair-share - "What do you think the position-time graph would look like for this rocket launch?"
• Discuss x velocity and y velocity
• Think-pair-share - what is changing, and what is the rocket experiencing throughout the launch trajectory?

The challenge in this lab lies in graphing and interpreting graphs, and those are both important skills to gain practice in as well -- primarily to become more comfortable with them. Students will likely need support and encouragement!

The next Scientist Spotlight is completed in this module. The goal of these is to showcase an array of scientists in fields relevant to the topics of the day, some from long ago and others young and active today, together representing a diversity of people who have all overcome some challenge in pursuit of their scientific passion.

A challenge about this topic is that most colleges and universities have access to some motion detector program, but not everyone does and different programs work differently. We've provided instructions using a few different resources that are free (tracker, PhET moving man simulation) and one resource that is paid (Vernier). If you're not sure whether your school has a Vernier license, I'd highly recommend checking in with whoever teaches physics at your institution, because that program is seamless and very easy to use both to connect with motion detectors (in the first activity) and to upload user-made videos (in the final extension activity)

Student worksheets are provided as part of the resources for these labs. Instructors can choose to use this worksheet in lieu of the science journal format. If using the science journal format, then powerpoint slides are all that is needed (no worksheet). We will often, but not always, provide student worksheets. In classes with time constraints, worksheets can be faster, but they do not ask your students to engage as deeply with the practices of science.

As always, students will complete an end-unit reflection:

• Read Aeon's pirate essay "How European Sailors Learned Celestial Navigation"
• Reflection Prompt: Consider pirates: evading capture by Naval vessels, hiding treasure on small islands, stalking and marauding trade ships, etc. Reflect on the navigational challenges pirates overcame to do these things. Especially consider aspects of position, velocity, and acceleration in your reflection. How do you feel about your understanding of these data? Has your comfort level (with regard to the process of science and/or to making graphs) changed since earlier in the course?

Sokoloff, David R., et al. Realtime Physics Active Learning Laboratories Module 1 Mechanics. John Wiley & Sons, 2012.

Aeon's pirate essay "How European Sailors Learned Celestial Navigation" is used for the Unit 4.1 Reflection Prompt.