If a cyclist takes one minute to complete half revolution on a circular path 120 m radius. What is the average velocity?

Options

A. 1 m/s
B. 2 m/s
C. 3 m/s
D. 4 m/s

Answer

To solve the problem of finding the average velocity of a cyclist who completes half a revolution on a circular path with a radius of 120 meters in one minute, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Motion**: The cyclist completes half a revolution on a circular path. This means that if we visualize the circular path, the cyclist starts from one point on the circumference and ends at the point directly opposite (diametrically opposite) after half a revolution.

2. **Calculate the Displacement**: The displacement is the straight-line distance between the starting point and the ending point. For half a revolution, this distance is equal to the diameter of the circle.
- The formula for the diameter \(D\) of a circle is:
\[ D = 2 \times R \]
- Given that the radius \(R\) is 120 meters:
\[ D = 2 \times 120 = 240 \text{ meters} \]

3. **Determine the Total Time**: The time taken to complete half a revolution is given as one minute. We need to convert this time into seconds for our calculations.
- Since 1 minute = 60 seconds, we have:
\[ \text{Total time} = 60 \text{ seconds} \]

4. **Calculate the Average Velocity**: The average velocity \(V_{avg}\) is defined as the total displacement divided by the total time taken.
- Using the formula:
\[ V_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}} \]
- Substituting the values we found:
\[ V_{avg} = \frac{240 \text{ meters}}{60 \text{ seconds}} = 4 \text{ meters/second} \]

5. **Conclusion**: Therefore, the average velocity of the cyclist is:
\[ V_{avg} = 4 \text{ m/s} \]