Graphical Representation of Motion

Position–time, velocity–time, and acceleration–time graphs help visualise motion. Slope and area under curves give velocity and displacement.

Position–time (x–t) graph

The position–time graph shows position (or displacement) on the vertical axis and time on the horizontal axis. The slope of the x–t graph at any point gives the velocity at that instant. A straight line means constant velocity; a curve means changing velocity.

Velocity–time (v–t) graph

The velocity–time graph shows velocity on the vertical axis and time on the horizontal. The slope of the v–t graph gives the acceleration. The area under the v–t graph (between the curve and the time axis) gives the displacement in that time interval. A horizontal line means constant velocity (zero acceleration).

Acceleration–time (a–t) graph

The acceleration–time graph shows acceleration versus time. The area under the a–t graph gives the change in velocity. For uniform acceleration, the a–t graph is a horizontal line. These three types of graphs are linked: from one we can derive the others using slope and area.

Link to simulator: The graph above is a velocity–time (or speed–time) representation; its slope is acceleration, its area is displacement.

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