A

To find the correct answer, we will evaluate each option based on the given velocity-time graph.
1. **Calculate the distance**: The distance covered by the cyclist can be found by calculating the area under the velocity-time graph. The graph shows three parts:

• **From 0 to 10 seconds**, the velocity is increasing from 0 to 10 m/s. The area is a triangle: A₁ = \frac{1}{2} \times 10 \times 10 = 50 m.
• **From 10 to 20 seconds**, the cyclist travels at a constant velocity of 10 m/s. The area is a rectangle: A₂ = 10 \times 10 = 100 m.
• **From 20 to 30 seconds**, the velocity decreases from 10 m/s to 0 m/s. The area is a triangle: A₃ = \frac{1}{2} \times 10 \times 10 = 50 m.

Therefore, the total distance = A₁ + A₂ + A₃ = 50 + 100 + 50 = 200 m. Hence, Option A stating the distance is 212.5 m is incorrect.
2. **Evaluate the other options**:

• **Option B** states the distance covered at a constant velocity (10 m/s) from 10 to 20 seconds is indeed 100 m.
• **Option C** states the velocity at t = 25s is 5 m/s, which is correct.
• **Option D** states the acceleration at t = 30s is 0 (since the velocity is constant), which is correct.

Thus, the incorrect statement is in Option A.