Reading graphs in context

Read the axis meaning first

On a distance-from-home graph, a falling section means returning towards home. On a total-distance-travelled graph, the vertical value cannot fall. A horizontal section means no change in that quantity.

A distance–time gradient gives speed when the distance is increasing along the route. For a return section, use the magnitude of the distance change to calculate speed. Average speed uses total distance travelled divided by total elapsed time, including stops.

On a speed–time graph, gradient gives acceleration and area under the graph gives distance travelled. Convert minutes to seconds or hours before combining units.

Here \(t\) is in seconds and \(v\) in metres per second. The three regions are a triangle, a rectangle and a triangle; their areas have units of metres.

A volume–time gradient gives filling or emptying rate. State the initial volume and any change in rate before constructing the graph.