Physics
Motion Graph Segment Calculator
Use graph geometry: gradient gives rate of change, and area under a velocity–time graph gives displacement.
Your measurements
Start with the example, or enter your own values. Use a dot for decimals and e for scientific notation.
Calculated locally. No account or uploads.
Result & working
ExampleThe calculator is loading. You can read the worked example below.
Step-by-step working
The formula
a = Δv/Δt
Δx = (v₁ + v₂)Δt/2 for a straight v–t segment
v_avg = Δx/Δt for a straight x–t segment
| Symbol | Meaning |
|---|---|
| Δt | Elapsed time t₂ − t₁. |
| a | Acceleration from the gradient of a velocity–time graph. |
| Δx | Signed displacement from the area under v–t. |
When to use this calculator
Use this for one straight graph segment. Curved graphs need a tangent for instantaneous gradient or numerical/graphical area methods.
Signed area below the time axis gives negative displacement. Distance travelled is not always the same as displacement.
Worked example
The calculator opens with these example values. All steps below are available even with JavaScript disabled.
- Δt = 4 − (0) = 4 s
- a = (v₂ − v₁)/Δt = (10 − (2))/4 = 2 m/s²
- Δx = area under straight v–t segment = (v₁ + v₂)Δt/2 = (2 + 10) × 4/2 = 24 m
a = 2 m/s²
Common mistakes
- Do not use graph height alone as acceleration.
- A position–time graph area has no standard displacement meaning; use its gradient for velocity.
- Ensure t₂ is later than t₁.