This tool draws a velocity-time graph from segments you enter and works out acceleration, displacement and distance for each one. It is for students who can plot a graph but hesitate over what the gradient and the area mean.
Free tool
Motion graph explorer
You can read points off a graph but mix up gradient, area, distance and displacement.
Everything you enter stays on this device.
Who is this tool for?
It suits Form 4 and Form 5 students in Mathematics, Science and Physics, who meet motion graphs in all 3 subjects. It also helps students who lose marks by answering with distance when the question asks for displacement.
How do I use it?
- Enter the starting velocity in m/s.
- For each segment, enter its duration in seconds and the velocity at its end in m/s.
- Add or remove segments, up to 6.
- Press Draw and calculate.
- Read the graph, the table and the totals, then open the interpretation questions and check your own answers.
How does it work?
The gradient of a velocity-time graph is acceleration: (change in velocity) ÷ (time taken). The area between the line and the time axis is displacement. For a straight segment the area is (u + v) ÷ 2 × t.
Area above the axis is positive and area below is negative. Distance uses the size of each area. When a line crosses zero, the tool splits the segment at that moment before adding the areas.
A short worked example
The starting example has 3 segments. It goes from 0 to 8 m/s in 4 s, stays at 8 m/s for 5 s, then changes to −4 m/s in 3 s.
The accelerations are 2, 0 and −4 m/s². The displacements are 16 m, 40 m and 6 m, which gives 62 m in total.
The third segment crosses zero after 2 s. It has an area of 8 m forwards and 2 m backwards, so its displacement is 6 m but its distance is 10 m. The total distance is 66 m.
What are the limits?
The tool handles straight-line motion with constant or uniformly changing velocity, up to 6 segments. It uses metres per second and seconds only, so convert your units before entering them.
It does not fit real data, and it does not draw displacement-time graphs. A zero or negative duration is rejected.
Where does this help in your subjects?
Try it with reading speed-time graphs and calculating distance from a speed-time graph. The page on distinguishing gradient from area targets the most common mix-up.
Then move to force and motion practice in Physics. For a teacher to go through graphs with you, see SPM Physics tuition and the one-hour trial class (from RM50).
Common questions
What is the difference between displacement and distance?
Displacement is the signed area under a velocity-time graph, so area below the axis counts as negative. Distance adds every area as a positive amount. They are equal only when the velocity never changes sign.
Why must every segment have a time greater than zero?
A segment of zero time would make acceleration undefined, because you would divide by zero. The tool rejects it with a message. A negative time has no meaning on this graph either.
Can I use this for a displacement-time graph?
No. This tool draws velocity-time graphs only. On a displacement-time graph the gradient is velocity, while here the gradient is acceleration and the area is displacement.
Does each segment start where the last one ended?
Yes. You enter the starting velocity once, then only the velocity at the end of each segment. This keeps the graph continuous, which is what a real moving object does.
If graphs make sense here but confuse you when an exam gives a shape you have not seen, a one-to-one lesson can build the habit of reading the axes and units first.
- Online one-to-one lessons for your child with an experienced teacher.
- Your first class is a one-hour trial, from RM50. The fee is agreed before you book.
- Happy with the teacher? Continue with lessons of about 1.5 hours. If not, ask for another teacher.