Acceleration Graphs

Objective: Calculate acceleration from a velocity graph.

On a one-dimensional velocity–time graph, slope Δv/Δt is average acceleration over a straight segment. A horizontal segment has zero acceleration but may have nonzero velocity and ongoing motion. A line with negative slope represents acceleration in the negative direction, not automatically slowing down; the speed trend depends on velocity sign. For velocity increasing from −2 m/s to +6 m/s in 4 s, acceleration is +2 m/s², and the object reverses when velocity passes through zero. Units of graph slope are m/s² when axes are m/s and s.

Objective: Apply acceleration graphs to calculations, evidence, and specified situations.

A velocity–time slope gives acceleration, and signed area gives displacement. An acceleration–time area gives velocity change. Straight velocity–time segments imply constant acceleration; horizontal velocity segments imply zero acceleration. A segment below the time axis contributes negative displacement, though distance remains nonnegative. Use the graph’s axis units and interval endpoints. To reconstruct position from velocity, an initial position is also needed; the velocity graph alone does not supply it.