GCSE(F), GCSE(H),

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?

Answer: 20ms^{-1}

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?

Answer: 8ms^{-1}

Speed for AC = gradient for AC = `frac(text(distance))((text(time))` `frac(800)(100) = 8ms^-1`

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