Unit 2: Speed at an instant
About this unit
The speed at an instant is the value that average speeds over shorter and shorter real stretches of time settle on, and that value is the derivative.
By the end, you can: Resolve the paradox of instantaneous speed: average over shorter and shorter real stretches of time and read off the value the averages settle on.
Modules
5 modulesLearn
- The paradox of instant speedArticle · Speed at an instant seems to be 0/0; instead average over short real stretches and see the averages settle (25, 20.5, 20.05… → 20 m/s).Not started
- Small, but never zeroArticle · Over a short stretch dt, ds ≈ s′(t)·dt with an error that shrinks faster than dt; dt is a real small amount, not zero, and zooming in makes the graph look straight.Not started
- Shrink the stretchExperiment · Slide the second point in until the secant's slope is within 0.5 of 20 m/s, and see the average speed is 20 + 5h.Not started
- Rates at an instantReview · Averages over shrinking stretches settle on the derivative; dt stays small but real; ds ≈ rate · dt.Not started