Figure 1 shows the speed-time graph of a cyclist moving on a straight road over a 7 s period - Edexcel - A-Level Maths Mechanics - Question 1 - 2006 - Paper 1

The section of the graph from t = 3 to t = 7 being parallel to the t-axis indicates that the cyclist is traveling at a constant speed during this time period, meaning there is no acceleration.

To calculate the distance travelled by the cyclist, we can break it down into two parts:

1. From t = 0 to t = 3 seconds: The speed increases from 0 to 5 m/s. The average speed for this period can be calculated as:

   $\text{Average Speed} = \frac{0 + 5}{2} = 2.5 \text{ m/s}$

   The distance covered in this interval is:

   $\text{Distance} = \text{Average Speed} \times \text{Time} = 2.5 \text{ m/s} \times 3 \text{ s} = 7.5 \text{ m}$

2. From t = 3 to t = 7 seconds: The speed is constant at 5 m/s for 4 seconds. The distance covered in this interval is:

   $\text{Distance} = \text{Speed} \times \text{Time} = 5 \text{ m/s} \times 4 \text{ s} = 20 \text{ m}$

The total distance travelled during the entire 7 seconds is:

$\text{Total Distance} = 7.5 \text{ m} + 20 \text{ m} = 27.5 \text{ m}$