A car runs at a constant speed on a circulat track of radius ` 100 m`. Taking `62.8 s` for every circular lap. The average velocity and average speed for each circular lap respectively are :

Options

A. (a) ` 10 m//s. 0`
B. (b) ` 0,0,
C. (c ) `0, 10 m//s`
D. (d) ` 10 m//s. 10 m//s`

Explanation

To solve the problem, we need to find the average velocity and average speed of a car running on a circular track with a radius of 100 meters, completing one lap in 62.8 seconds.

### Step-by-Step Solution:

1. **Understanding the Circular Motion**:
- The car is moving in a circular path, which means it returns to its starting point after completing one full lap.

2. **Calculating the Displacement**:
- Displacement is defined as the change in position. After completing one full lap, the car returns to its original position.
- Therefore, the displacement after one circular lap is **0 meters**.

3. **Calculating the Average Velocity**:
- Average velocity is given by the formula:
\[ \text{Average Velocity} = \frac{\text{Displacement}}{\text{Time}} \]
- Substituting the values:
\[ \text{Average Velocity} = \frac{0 \, \text{m}}{62.8 \, \text{s}} = 0 \, \text{m/s} \]

4. **Calculating the Circumference of the Circular Track**:
- The distance covered in one lap (circumference) is calculated using the formula:
\[ \text{Circumference} = 2\pi r \]
- Where \( r = 100 \, \text{m} \):
\[ \text{Circumference} = 2 \times \pi \times 100 = 200\pi \approx 628.0 \, \text{m} \]

5. **Calculating the Average Speed**:
- Average speed is defined as the total distance traveled divided by the total time taken:
\[ \text{Average Speed} = \frac{\text{Distance}}{\text{Time}} \]
- Substituting the values:
\[ \text{Average Speed} = \frac{628.0 \, \text{m}}{62.8 \, \text{s}} = 10 \, \text{m/s} \]

### Final Answers:
- **Average Velocity**: \( 0 \, \text{m/s} \)
- **Average Speed**: \( 10 \, \text{m/s} \)