This tool takes the corner points of a straight-line speed-time or velocity-time graph and works out the gradient (acceleration) and the area under each segment. It then totals distance and, for velocity, displacement. If you add a mass, it also gives kinetic energy at the start and end.
It follows the two rules that most marks depend on: the gradient is acceleration, and the area is distance or displacement.
How do I use it?
- Type the points, one per line, as “time, value” with time in seconds and value in m/s. For example “0, 0” on the first line and “5, 10” on the second.
- Keep the times increasing. Straight lines join consecutive points.
- Choose what the vertical axis shows: speed (no direction) or velocity (negative means the opposite direction).
- Add a mass in kg if you want kinetic energy. Leave it empty otherwise.
- Press Analyse graph. Reset restores the starting points.
Example walk-through
The tool opens with 0, 0 and 5, 10 as speed. The table shows one segment from 0 to 5 s with acceleration 2 m/s² and area 25 m.
The total distance is 25 m in 5 s, so the average speed is 5 m/s. Because the axis is speed, the tool says displacement cannot be found.
Add a mass of 2 kg. The kinetic energy is 0 J at the start and ½ × 2 × 10² = 100 J at the end, a change of 100 J.
Now switch to velocity with three points: 0, 0 then 4, 8 then 8, -8. Segment 1 has acceleration 2 m/s² and area 16 m. Segment 2 goes from 8 to -8 m/s in 4 s, so the acceleration is -4 m/s² and the net area is 0 m.
The object turns round halfway through segment 2, at 2 s in. The tool splits the segment at that crossing, so the distance is 16 m for this segment and the total is 32 m in 8 s. The displacement is 16 + 0 = 16 m forward.
How do I read the result?
- Acceleration column: the gradient of each segment, in m/s². A negative value means the speed or velocity is decreasing.
- Area column: shown as distance for speed data, and as signed area for velocity data.
- Total distance and average speed: distance divided by total time.
- Displacement line: only for velocity, with a negative value meaning the final position is behind the start.
What are the limits?
Only straight segments between points are supported, so curved graphs must be approximated by a list of points. Speed cannot be negative, and the tool says so if you try.
Speed-only data can never give displacement direction. Check that your units are seconds and m/s before comparing with a textbook answer, and confirm what your syllabus expects on the Cambridge subject page.
Which lessons explain the output?
Begin with calculating speed over a segment and comparing distance-time and speed-time graphs. Then read finding acceleration from a gradient, area under a speed-time graph and displacement versus total distance. If you mix distance and displacement, see the clinic page on that.
Kinetic energy links to tracking energy stores. Extra questions are in the motion and graphs practice set, and the graph-reading checklist works for any graph. See the tools page for the rest.
When the routine still breaks on harder graphs, our team can work through them with you. See online one-to-one Physics tuition for how that works.