Graphs in practical situations

• Use and interpret travel graphs and conversion graphs.
• Draw graphs from given data.
• Apply rate of change to distance–time and speed–time graphs, including acceleration and deceleration.
• Calculate distance travelled as the area under a speed–time graph (linear sections only).
• Estimate and interpret the gradient of a tangent at a point on a curve.

Gradient = speed

Time is on the horizontal axis and distance from a starting point on the vertical axis. A straight sloping section means constant speed; its gradient is the speed. A horizontal section means the object is stationary. A section sloping down means it is returning towards the start. The steeper the line, the faster the speed.

Read across, then down

A conversion graph is a straight line, often through the origin. To convert, go from the value on one axis to the line, then across (or down) to the other axis. To draw a graph from a table of data, choose sensible scales, label both axes with units, plot each point accurately and join with a ruler if the relationship is linear.

Gradient = acceleration; area = distance

On a speed–time graph the gradient is the acceleration (in m/s²). A negative gradient is a deceleration. A horizontal section means constant speed. The area under the graph is the distance travelled: split it into triangles, rectangles and trapezia.