On a distance-time graph, the gradient of the graph gives the speed or velocity of the object being measured:
`text(speed) = frac(text(distance))(text(time))`
The first 40 metres (AB) is covered at a constant speed of `frac(20)(40)` = 0.5ms-1. The next 20 metres (BC) is covered at a rate of `frac(20)(40)` = 2. The gradient of the graph gives the rate of change of distance against time.
The average rate of change can also be determined from a graph. In this instance, the average rate of change gives the average speed. The average speed for the distance is given by the gradient of the line joining the two points over which the average speed is measured (AE), which is `frac(80)(100)` = 0.8ms-1.
1. A car moves at a constant speed from stationary for a distance of 400m as shown on the graph, below. What is the speed of the car in this part of the journey?
Speed for first 400m = gradient for AB = `frac(text(distance))(text(time)) = frac(400)(20) = 20ms^-1`
2. Using the graph, what is the average speed for the first 800m?
Speed for AC = gradient for AC = `frac(text(distance))((text(time))` `frac(800)(100) = 8ms^-1`