Enter time and velocity points to study motion. See slopes, areas, averages, and segment changes. Export results quickly for homework, revision, audits, and teaching.
This sample shows a motion that speeds up, slows down, stops, and then reverses. You can load these values into the form using the example button.
| Point | Time (s) | Velocity (m/s) |
|---|---|---|
| 1 | 0 | 0 |
| 2 | 2 | 4 |
| 3 | 4 | 6 |
| 4 | 6 | 3 |
| 5 | 8 | 0 |
| 6 | 10 | -2 |
A V-T graph calculator helps you study motion by reading velocity against time across several points. Instead of solving only one direct equation, this page handles piecewise motion, segment slopes, signed area, total distance, average speed, average velocity, and local acceleration.
When you enter ordered points, the calculator joins them with straight segments. Each segment represents a constant rate of change in velocity over its own interval. That makes the tool useful for classwork, graph interpretation, checks, and quick motion summaries.
The result area appears before the form after submission. This layout lets you inspect the graph, metrics, and segment table immediately. You can then return to the form, revise values, and calculate again without losing the page structure.
The export options help you keep a clean record. CSV is useful for spreadsheets and later analysis. PDF is useful for homework files, revision packs, printouts, and project notes. The example table also gives a ready starting dataset for testing the page.
Segment acceleration: a = (v₂ - v₁) / (t₂ - t₁)
Segment displacement: s = ((v₁ + v₂) / 2) × (t₂ - t₁)
Total displacement: sum of all signed segment displacements
Total distance: sum of absolute motion lengths, including zero-crossing splits when direction changes
Average velocity: total displacement / total time
Average speed: total distance / total time
Overall average acceleration: (final velocity - initial velocity) / total time
Graph meaning: slope gives acceleration, and area under the line gives displacement.
Step 1: Enter a motion label if you want a named report.
Step 2: Set the time and velocity units that match your question.
Step 3: Fill at least two point rows with increasing time values.
Step 4: Add more rows when the motion changes between intervals.
Step 5: Enter an optional query time to inspect a value inside the graph range.
Step 6: Press the calculate button and review the result section above the form.
Step 7: Read the summary, point table, segment analysis, and graph together.
Step 8: Use CSV or PDF export when you need a saved copy.
It shows velocity on the vertical axis and time on the horizontal axis. The slope gives acceleration, while the area under the graph gives displacement.
Displacement comes from the signed area under the velocity-time line. Positive regions add forward motion, while negative regions subtract because the direction reverses.
Displacement keeps direction signs. Distance ignores direction and adds total path length. This calculator handles both, even when the graph crosses zero velocity.
A V-T graph moves forward along the time axis. Equal or descending times would break segment width, slope calculation, and area measurement.
It estimates velocity and displacement at one chosen time inside the graph range. The value is found by linear interpolation within the matching segment.
Yes. Negative velocities show motion in the opposite direction. The calculator uses them in slopes, signed area, distance splitting, and direction-change checks.
This page joins entered points with straight segments. That makes each interval piecewise linear, which is excellent for many graph problems and classroom exercises.
Use CSV for spreadsheet work, recalculation, and sorting. Use PDF for fixed reports, printouts, homework submission, and clean visual sharing.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.