The graph shows the velocity of a particle over the first 20 minutes of its motion - OCR - GCSE Maths - Question 19 - 2023 - Paper 4

From the graph, the velocity from 0 to 7 minutes is 0 m/min. Thus, the distance travelled in this segment is:

Distance = Velocity × Time = 0 m/min × 7 min = 0 m

Between 7 and 15 minutes, the velocity is v m/min. Therefore, the distance travelled in this segment is:

Distance = v m/min × (15 min - 7 min) = v m/min × 8 min = 8v m

From 15 to 20 minutes, the velocity is 0 m/min. Thus, the distance travelled in this segment is:

Distance = Velocity × Time = 0 m/min × (20 min - 15 min) = 0 m

The total distance is the sum of distances from all segments:

Total Distance = Distance (0 to 7 min) + Distance (7 to 15 min) + Distance (15 to 20 min)

This gives us:

231 m = 0 m + 8v m + 0 m

Thus, 231 m = 8v m

To find v, we can rearrange the equation:

8v = 231

Dividing both sides by 8 gives:

v = rac{231}{8} = 28.875 m/min