Motion Graph Interpretation
Overview
x–t graph: slope = velocity; straight line = constant v; curve = acceleration; horizontal = at rest. v–t graph: slope = acceleration; area = displacement; horizontal = constant v (a=0); straight diagonal = UAM. a–t graph: area = change in velocity; horizontal line = constant a (UAM); at zero = constant velocity. Examiner tip: always state units on graph axes, and use the word 'slope' not 'gradient' in IB/school contexts — both are acceptable. If v–t graph has a negative slope, the object decelerates (or accelerates in the negative direction).
The three motion graphs and what they mean
Position–time (x–t): slope at any point = instantaneous velocity. A straight line = uniform motion; a curve = changing velocity; concave up = accelerating; concave down = decelerating. Velocity–time (v–t): slope = acceleration; area under graph = displacement (positive area if v > 0, negative if v < 0). Acceleration–time (a–t): area under graph = change in velocity.
Reading non-uniform motion graphs
For a v–t graph with a changing slope (non-constant acceleration), the displacement is still found as the area under the curve — use geometry (triangles, trapezoids) or count squares. The instantaneous acceleration at any point is the tangent slope. If the v–t graph returns to zero, the object has returned to the same speed but possibly from a different direction. Watch sign: negative v means motion in the negative direction.
- ⚠Confusing the slope of x–t (which gives velocity) with the slope of v–t (which gives acceleration)
- ⚠Calculating distance instead of displacement — displacement uses signed areas
- ⚠Thinking a v–t graph reaching zero means the object is back at the start — it only means zero velocity momentarily