RecallWeave · a motion lab
Rates become change.
Trace a velocity curve and watch its area become displacement. Then reverse direction: what cancels, and what keeps adding up?
1. Choose a curve
A return trip still covers distance.
For Out and back, inspect 4 s and then 8 s. Predict the final displacement before you look at the distance.
Connect 2–8 points with straight lines. Begin at 0 s; use increasing whole seconds through 120 s. Velocity may be −50 to 50 m/s, with one decimal place.
These are authored mathematical curves. A point gives an instantaneous velocity; the area over an interval gives a change in position.
What does editing change?
Any point edit clears the previous result. Apply the whole curve to calculate again. Nothing is saved automatically or sent anywhere.
2. Inspect a moment
Move in tenths of a second. The slider also accepts arrow, Home and End keys.
Velocity and signed area
Two ways of accumulating the same motion
Curves below the velocity plot use samples 0.1 s apart. Graph coordinates and labels are approximate. Exact fractions are retained in the readout, table and download.
See every interval's contribution
Rows include all authored intervals. The two “so far” columns stop at the selected time; a shaded row is only partly covered. A zero crossing inside a segment is calculated exactly, even between slider positions.
| Interval (s) | Endpoint velocities (m/s) | Zero inside interval (s) | Displacement so far (m) | Distance so far (m) | Whole interval (m) |
|---|
Turn the picture into an explanation
3. Study the connections
Work through twelve original questions about units, signed area, direction changes and local versus average rates.
- Download the lesson JSON.
- Open RecallWeave's learning page and choose the file under Bring your own lesson.
- Review the preview and choose Start this deck. First answers, review and later practice stay separate.
The explorer is self-contained. To study offline, also keep RecallWeave's separate demo.html file. A script running through the questions does not measure a learning gain.
Try a zero between the ticks
Set two points: (0 s, 1 m/s) and (1 s, −2 m/s).
The velocity crosses zero at 1/3 s. At the end, net displacement is −1/2 m, but distance is 5/6 m.
Explain why taking the absolute value of the final displacement would miss some of the travel.