Resistance Is Not Futile: Air Resistance in an Algebra-Based Course
Why this work is in the frame
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Bibliographic record
Abstract
In this paper we show that an object's terminal speed due to air resistance depends not on any of the object's details, but only on the distance at which an object reaches a particular fraction of its terminal speed. We show this graphically and algebraically. Although a mathematical treatment of air resistance is beyond the scope of an algebra-based, introductory physics course, some of the concepts involved are important for (at least) three reasons. First, the equations used for uniform acceleration only approximately (and perhaps badly!) describe projectiles students know (a home-run baseball, for example). With the equation for terminal speed, students can estimate the speeds at which the simple kinematic equations no longer produce “reasonable” approximations.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it