11.6 Gradients and areas under graphs — Learn

Prerequisites: calculate triangle and rectangle areas and interpret graph axes.

Objectives

By the end of this section, you can calculate gradients and areas under graphs, then interpret each result with units.

Gradient and area on rate graphs

On a velocity-time graph, the gradient is acceleration: change in velocity divided by change in time. The area under the graph is distance travelled. For a straight rising section, split the area into familiar shapes and add them.

Worked example. Velocity rises evenly from 0 m/s to 8 m/s over 4 s. The area is a triangle.

The units are seconds multiplied by metres per second, which gives metres.

Watch out. The gradient and area answer different questions. The gradient gives acceleration in m/s²; the area gives distance in metres. Check the requested quantity and units.

Progress check

The station walk is constant speed, so its distance-time graph is a straight line. At 60 minutes, the distance is 4 km.

You should now be able to

• calculate gradients and areas under graphs, then interpret each result with units.;
• check your result by substitution or by interpreting the graph;
• explain the method in your own words.