## Approximate Distance Travelled and Speed

The area under a velocity time graph is the distance travelled. Sometimes the graph is not made up of straight lines and we must find an approximation for the area.We can divide the graph up into trapezia - one for each second. In the first second the distance travelled is approximately

\[\frac{1}{2}(0+4.4) \times 1=2.2m\]

.In the second second the distance travelled is approximately

\[\frac{1}{2}(4.4+6.4) \times 1=5.4m\]

.In the third second the distance travelled is approximately

\[\frac{1}{2}(6.4+7.8) \times 1=7.1m\]

.In the fourth second the distance travelled is approximately

\[\frac{1}{2}(7.8+9.0) \times 1=8.4m\]

.The total distance travelled is

\[2.2+5.4+7.1+8.4=23.7m\]

.The average speed is approximately

\[\frac{23.7}{4}=5.9 m/s\]

.