A velocity-time graph plots signed velocity on the vertical axis against time on the horizontal axis.
The ordinate gives instantaneous velocity. Values above and below the time axis represent motion in opposite directions. Crossing the time axis indicates a change of direction only when velocity changes sign.
The gradient gives acceleration. A horizontal line means constant velocity and zero acceleration; a straight non-horizontal line means constant acceleration; a changing gradient means non-uniform acceleration.
The gradient of a chord gives average acceleration,
The gradient of a tangent estimates instantaneous acceleration. Displacement over an interval is the signed area between the graph and the time axis,
Distance travelled is found by adding the magnitudes of the separate areas, equivalently by finding the area under a speed-time graph.
For calculus-based courses, the same signed-area relationship may be written
This integral notation is an extension of the graphical meaning. IB Physics and AP Physics 1 questions can use geometric signed areas without requiring calculus.