A particle moves along a semicircle of radius `10m` in 5 seconds. The average velocity of the particle is

Options

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

Answer

To find the average velocity of a particle moving along a semicircle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Motion**: The particle moves along a semicircle with a radius of 10 meters.

2. **Determine the Total Time**: The total time taken for the motion is given as 5 seconds.

3. **Calculate the Displacement**:
- Displacement is defined as the shortest distance between the initial and final positions of the particle.
- Since the particle moves along a semicircle, its initial position is one end of the diameter and the final position is the other end of the diameter.
- The diameter of the semicircle can be calculated using the formula:
\[ \text{Diameter} = 2 \times \text{Radius} = 2 \times 10 \, \text{m} = 20 \, \text{m} \]
- Therefore, the total displacement is 20 meters.

4. **Calculate the Average Velocity**:
- The formula for average velocity (\(v_{avg}\)) is given by:
\[ v_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}} \]
- Substituting the values we have:
\[ v_{avg} = \frac{20 \, \text{m}}{5 \, \text{s}} = 4 \, \text{m/s} \]

### Final Answer:
The average velocity of the particle is **4 m/s**.

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