Introductory Mathematics
How fast was the traveller moving?
Shorter time does not mean slower travel
The traveller's position readings get closer together in time. Botie wants to see what their average speeds say about the starting moment.
BOTIE
The inputs we are comparing
Earlier position (metres)
Same in both cases
4
Later position (metres)
One-second interval
9
Tenth-second interval
4.41
Earlier time (seconds)
Same in both cases
2
Later time (seconds)
One-second interval
3
Tenth-second interval
2.1
Result for one-second interval
5
The same path later in the journey
This check uses the pieces from “Measure movement per elapsed second”.
BOTIE
- Earlier position (metres)
9
- Later position (metres)
16
- Earlier time (seconds)
3
- Later time (seconds)
4
Use a number, text, or an array matching the requested result. For a matrix, put each row in brackets. Saving your prediction runs your current construction on these inputs and checks the earlier examples too.
Build a construction in the workspace above first. This case will test those pieces.
Why does a very short interval still give an average, and why can you not obtain instantaneous speed by setting elapsed time to zero?
A derivative describes a limit of change-per-input ratios. A measured finite interval only approximates it.
Each result is an average over a nonzero interval. Instantaneous speed is the limit of these averages, not an average computed by dividing by zero.
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