Motion Graphs

Objective: Interpret position, direction, and velocity from graph slope.

On a position–time graph, slope Δx/Δt is average velocity over an interval. A straight line has constant velocity; a horizontal line means constant position, not zero position. A positive slope corresponds to positive velocity under the chosen axis; a negative slope to negative velocity. A curve’s instantaneous velocity is its tangent slope at a point. The vertical intercept is the initial position at t = 0.

Objective: Interpret acceleration and signed displacement from velocity graphs.

On a velocity–time graph, slope Δv/Δt is average acceleration. The signed area under the curve over a time interval is displacement: positive regions add, negative regions subtract. The sum of absolute areas is distance traveled when motion is along one axis. A horizontal line represents constant velocity; a line along v = 0 represents rest. Crossing v = 0 may indicate a reversal when velocity changes sign.

Objective: Check graph units, stops, reversals, and consistency.

A graph must be interpreted from its labeled axes, units, and reference convention. Position–time slope corresponds to velocity, while velocity–time slope corresponds to acceleration; the two slopes are not interchangeable. A turnaround occurs when velocity changes sign, or when a position–time graph reverses slope. For piecewise motion, analyze each segment before adding total displacement or distance. Avoid inferring a physical path shape from the shape of a time graph.