A cyclist moving on a circular track of radius 40 m completes half a revolution in 40 s. Its average velocity is

Options

A. zero
B. `4pi ms^(-1)`
C. `2ms^(-1)`
D. `8pi ms^(-1)`

Explanation

To find the average velocity of a cyclist moving on a circular track, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: The cyclist completes half a revolution on a circular track with a radius of 40 meters in 40 seconds. We need to calculate the average velocity, which is defined as the total displacement divided by the total time taken.

2. **Identify the Displacement**:
- The cyclist starts at point A and ends at point B after half a revolution.
- The displacement is the straight-line distance from point A to point B, which is the diameter of the circle.
- The formula for the diameter (D) of a circle is:
\[ D = 2R \]
- Given that the radius (R) is 40 meters, we can calculate the diameter:
\[ D = 2 \times 40 \, \text{m} = 80 \, \text{m} \]

3. **Calculate the Average Velocity**:
- The average velocity (V_avg) is calculated using the formula:
\[ V_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}} \]
- We know the total displacement is 80 meters (diameter) and the total time taken is 40 seconds. Plugging in these values:
\[ V_{avg} = \frac{80 \, \text{m}}{40 \, \text{s}} = 2 \, \text{m/s} \]

4. **Final Answer**: The average velocity of the cyclist is:
\[ \text{Average Velocity} = 2 \, \text{m/s} \]