Before generation
Use this planner before a motion investigation to check whether sampling intervals and position resolution can show the expected movement, rest, and direction changes. It calculates the average slope of every planned segment and compares displacement magnitude with the measurement increment. This helps identify sparse timing or movements smaller than the apparatus can resolve. It does not simulate acceleration inside an interval, guarantee constant velocity, or prove that a zero endpoint displacement means rest.
Worked example
The fictional cart moves from 0.00 to 0.80 m during two one-second intervals, stays at 0.80 m for one interval, then moves back to 0.30 m across two intervals. With 0.01 m resolution, every moving displacement spans at least twenty-five resolution steps. The report shows positive motion, planned rest, and negative motion, identifies uniform one-second sampling, and keeps the rest warning visible because unobserved movement could occur between equal endpoints.
Formula or methodology
For each chronological interval, duration equals ending time minus starting time, signed displacement equals ending position minus starting position, and average interval velocity equals displacement divided by duration. Resolution ratio equals absolute displacement divided by position resolution. A moving interval is flagged feasible when it spans at least two resolution increments. Sampling is uniform when all interval durations match within a tight numeric tolerance.
How to interpret the result
A positive velocity follows the defined positive axis, a negative velocity points oppositely, and zero means only that sampled endpoints match. A reversal count requires adjacent nonzero velocities with different signs; a rest segment between directions is reported separately. A low resolution ratio suggests finer position measurement, longer duration, greater displacement, or another method. Even a large ratio says nothing about timing precision, calibration, alignment, or motion between samples.
Common mistakes
Do not confuse position with distance, use speed when direction matters, join unordered times without sorting, divide by zero-duration intervals, infer rest from two equal endpoints without observing between them, or claim the interval slope is instantaneous velocity. Define origin and positive direction, choose a sampling rate that can reveal changes, keep time and position units consistent, test apparatus response, record uncertainty, and follow the approved practical risk assessment.
