The prediction activity lets students choose Ground, moving observer B or stationary observer C, enter three positions and a displacement, and check the numbers against the model. Switching frame clears the old prediction while preserving the trajectories. The observer changes the coordinates, not the motion model.
Declare the direction, unit, and clock
Use one-dimensional positions in meters, positive to the right. All records use the same times t=0, 1, and 2 seconds. Over the interval 0..2 seconds, define:
Object A: x_A(t) = 1 + 2t
Moving observer B: x_B(t) = 2t
Stationary observer C: x_C(t) = 6
Ground origin: x_G(t) = 0
OpenStax's relative-motion explanation describes reference frames and displacement as final position minus initial position. This activity uses those relationships with its own trajectories and records; it does not copy the source's labs, pictures, or worked stories.
Use this ground-coordinate key:
| Time, seconds | A position, m | B position, m | C position, m |
|---|---|---|---|
| 0 | 1 | 0 | 6 |
| 1 | 3 | 2 | 6 |
| 2 | 5 | 4 | 6 |
The lines are explicitly supplied throughout the interval, not inferred from three measured observations. Nothing in this model establishes a force, a physical trial, or a learner's actual response.
Predict before revealing the frame key
Give learners a blank table with the observer, time, A's predicted relative position, and a final-minus-initial displacement line. Ask: “Does A change position relative to this observer from t=0 to t=2? Show the two positions you used.”
Keep this answer sheet separate from the completed teacher key. A learner choosing the ground origin and a learner choosing B must name those frames so their different numbers can be interpreted.
For this model, calculate position relative to an observer at the same time:
x_relative(t) = x_A(t) − x_observer(t)
Subtracting B's t=0 position from A's t=2 position would mix different times and answer a different question. Align the rows first.
Compare three valid descriptions
| Frame used for A | Position at t=0 | Position at t=1 | Position at t=2 | Displacement, t=0..2 |
|---|---|---|---|---|
| Ground G | 1 m | 3 m | 5 m | +4 m |
| Moving B | 1 m | 1 m | 1 m | 0 m |
| Stationary C | −5 m | −3 m | −1 m | +4 m |
Ground displacement is 5−1=+4 m. Relative to B, A remains one meter to B's right: (1+2t)−2t=1. Its relative displacement is 1−1=0 m. B and A move together in the supplied model, so a constant separation is consistent with ground motion.
Relative to C, the initial and final positions are 1−6=−5 m and 5−6=−1 m. The displacement is −1−(−5)=+4 m. Shifting the stationary origin changed the positions, while leaving this displacement unchanged.
The negative C-relative positions mean A is left of C's origin. They are not negative traveled distances. At the end of the interval A is still left of C but has moved rightward relative to C. Keep position sign, change in position, and distance language separate.
No frame is a universal answer key detached from its label. The ground, B, and C rows are all valid descriptions of the declared trajectories.
Make the game an explanation task
Pair learners who predicted different frame-relative outcomes. Each partner identifies the observer, reads the initial and final positions, and explains the subtraction. Use a blank reasoning stem:
“Relative to ___, A starts at ___ m and ends at ___ m. The displacement is ___ m because ___. The ground trajectories did / did not change when I changed frames.”
The teacher reads the actual reasoning and evidence rather than converting a correct number into a mastery score. Leave real class responses, timing, supports, and required standards or materials unfilled until supplied.
An optional original diagram can show A and the selected observer at each shared time with a signed axis and unit labels. The diagram should match the listed coordinates. Changing frame changes the displayed coordinate origin, not the physical trajectory formulas.
Try the prediction view
Choose B and predict A’s positions at 0, 1 and 2 seconds. Enter one in all three fields and zero displacement, then press Check prediction. The result shows both the time-aligned subtraction and the final-minus-initial change. A blank entry is missing; an entered zero is a valid value.
Choose C next and use negative five, negative three and negative one. The displacement is still positive four. Explain why the negative positions place A left of C while the positive displacement describes a rightward change. Review the explanation separately from the number check. The activity does not grade prose, collect sensor readings or report a physical experiment.
Copy this prompt
Build an original reference-frame prediction game with one-dimensional positions in meters, positive right and a shared clock t=0,1,2 seconds. Fixed trajectories throughout 0–2 seconds: A=1+2t, observer B=2t, stationary observer C=6, ground origin G=0. Show the ground-coordinate table A 1/3/5, B 0/2/4 and C 6/6/6.
Native Ground, B and C buttons select the observer for A. Supply four blank prediction fields: relative position at each time and displacement from t=0 to t=2. Ground key is 1,3,5 with displacement +4. B key is 1,1,1 with displacement 0. C key is -5,-3,-1 with displacement +4. Compare A and observer at the same time, then final minus initial. Negative position means left of the origin, not negative traveled distance.
Check prediction requires complete finite numeric entries, treating zero as valid and blank as missing. Show a precise numeric comparison and the corresponding subtraction without automatically grading a written explanation. Frame changes clear predictions and feedback; editing a prediction clears feedback. Reset returns to Ground with blank fields. Provide a separate preparation key and a blank reasoning note. The model is supplied mathematics, not a measured experiment or force analysis.
Return one complete HTML file. Keep the position table, selected observer and prediction fields together. Use readable coordinate labels and show each matching-time subtraction beside the displacement calculation. Stack the table and answers on a phone. A frame change clears the predictions, while a written explanation remains for teacher discussion.
Compare the two apparently conflicting answers
Keep the prediction sheet, model key and teacher-reviewed explanations in your lesson files. Have partners read their observer names before sharing their numbers. For a frame-comparison walkthrough, NOS can render the prepared HTML with the observer name beside every result. Start with Ground and B, then ask why C shifts every position without changing the four-meter displacement.