Extract velocity, acceleration and signed displacement from motion graphs.
Method and worked examples
On a position–time graph, gradient gives velocity. A horizontal section means rest and a negative gradient means motion in the negative direction. A tangent to a curve gives instantaneous velocity, whereas a chord gives average velocity over an interval. The graph is not a drawing of the physical path.
On a velocity–time graph, gradient is acceleration and signed area is displacement. Areas below the time axis are negative; add their magnitudes when calculating distance. On an acceleration–time graph, signed area gives velocity change. Label quantities and units, and calculate a gradient using two well-separated points from the relevant straight section. Do not confuse zero velocity with zero gradient.
Example 1
Velocity increases linearly from 2.0 to 8.0m/s in 3.0s. Find acceleration and displacement.
Gradient a=38−2=2.0m/s2. Area is a trapezium: displacement =(2+8)×23=15m.
Example 2
A cart moves at+3m/s for 2s, then −2m/s for 3s. Find displacement and distance.
Signed area =3×2−2×3=0m. Distance adds magnitudes: 6+6=12m. The cart returns to its start.
Watch out:The gradient tells acceleration. An object can have positive velocity while a negative gradient shows it slowing down.
2. Motion graphs and evidence | Year 11 Physics | Ascent Arcade