Displacement–time graphs

A displacement–time graph is a record of position, not a picture of the road. Its vertical coordinate tells you where the particle is; its gradient tells you how quickly and in which direction that position is changing.

Gradient means vertical change divided by horizontal change. The symbol $\Delta$ means “change in”, calculated as final value minus initial value.

A secant joins two points and gives average velocity over an interval. A tangent touches the curve at one instant and gives the instantaneous velocity there.

A displacement–time graph consists of straight segments joining $(0,0)$, $(4,12)$, $(7,12)$ and $(10,6)$, with time in seconds and displacement in metres. Find the velocity on each stage and state when the particle is at rest.

From 0 to 4 s: