Read what “distance” means on the vertical axis. Total distance travelled cannot decrease. Distance from home can decrease during a return journey. For straight-line travel along the route, speed is the magnitude of the gradient of a distance-from-home graph. A horizontal section means the traveller is stationary. Example A walker goes 2 km from home in 20 minutes, rests for 10 minutes, then returns in 40 minutes. The graph uses minutes horizontally and distance from home in kilometres vertically. Outward speed is 2 2060=6 km/h; return speed is 2 4060=3 km/h. Average speed is 4 7060= 247 3.43 km/h, including the rest. The cumulative distances at 0,20,30,70 minutes are 0,2,2,4 km. The corresponding speed graph is horizontal at 6, then 0, then 3 km/h on those three time intervals. A curved distance graph needs a tangent to estimate speed at one instant.

Read what “distance” means on the vertical axis. Total distance travelled cannot decrease. Distance from home can decrease during a return journey. For straight-line travel along the route, speed is the magnitude of the gradient of a distance-from-home graph. A horizontal section means the traveller is stationary.

A walker goes \(2\) km from home in \(20\) minutes, rests for \(10\) minutes, then returns in \(40\) minutes. The graph uses minutes horizontally and distance from home in kilometres vertically.

Outward speed is \(\dfrac2{\dfrac{20}{60}}=6\) km/h; return speed is \(\dfrac2{\dfrac{40}{60}}=3\) km/h. Average speed is \(\dfrac4{\dfrac{70}{60}}=\dfrac{24}{7}\approx3.43\) km/h, including the rest.

The cumulative distances at \(0,20,30,70\) minutes are \(0,2,2,4\) km. The corresponding speed graph is horizontal at \(6\), then \(0\), then \(3\) km/h on those three time intervals. A curved distance graph needs a tangent to estimate speed at one instant.

Distance–time graphs and return journeys

Distance–time graphs and return journeys