Graphs of Motion

Graphs turn columns of numbers into a picture of how an object moves, and reading them fluently is one of the most transferable skills in physics. The three graphs you must interpret are displacement–time, velocity–time, and acceleration–time. The connections between them come down to two operations: taking a gradient and finding an area.

Displacement–time graphs

On a displacement–time ($s$–$t$) graph, the vertical axis records position and the horizontal axis records time. The gradient of the line equals the velocity, because velocity is $\Delta s / \Delta t$. A horizontal line means the object is stationary. A straight sloping line means constant velocity. A curve means changing velocity, that is, acceleration. To find the instantaneous velocity at a point on a curve, draw a tangent to t