A pair of cameras is used on a motorway to help determine the average speed of vehicles travelling between the two cameras - AQA - A-Level Physics - Question 4 - 2020 - Paper 1

To find the average speed of the car, we calculate the area under the speed–time graph shown in Figure 5. The graph is composed of three segments:

1. A triangle (0 to 1 minutes) with base 1 minute and height 15 m s⁻¹, yielding an area of:

   $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 1 \times 15 = 7.5 \text{ m}$

2. A rectangle (1 to 2.5 minutes) with width 1.5 minutes and height 25 m s⁻¹, yielding an area of:

   $\text{Area} = \text{width} \times \text{height} = 1.5 \times 25 = 37.5 \text{ m}$

3. A triangle (2.5 to 4 minutes) with base 1.5 minutes and height 25 m s⁻¹, yielding an area of:

   $\text{Area} = \frac{1}{2} \times 1.5 \times 25 = 18.75 \text{ m}$

Adding these areas together, the total distance travelled is: $\text{Total distance} = 7.5 + 37.5 + 18.75 = 63.75 \text{ m}$

To find the average speed, we divide the total distance by the total time (4 minutes): $\text{Average speed} = \frac{63.75 \text{ m}}{4 \text{ min}} = \frac{63.75 \text{ m}}{240 \text{ s}} = 0.26562 \text{ m s}^{-1}$

Since 0.26562 m s⁻¹ is less than 22 m s⁻¹, we conclude that the average speed of the car did not exceed the speed limit.