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. 0,0
B. 0,10m/s
C. 10 m/s, 10 m/s
D. 10 m/s, 0

Answer

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 Average Velocity**:
- Average velocity is defined as the total displacement divided by the total time taken.
- Displacement is the shortest distance from the initial position to the final position. Since the car completes one full lap on a circular track, its initial and final positions are the same.

\[ \text{Displacement} = 0 \, \text{m} \quad (\text{since initial position = final position}) \]

\[ \text{Time} = 62.8 \, \text{s} \]

\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{0 \, \text{m}}{62.8 \, \text{s}} = 0 \, \text{m/s} \]

2. **Calculating Average Speed**:
- Average speed is defined as the total distance traveled divided by the total time taken.
- The distance traveled in one complete lap is the circumference of the circular track, which can be calculated using the formula:

\[ \text{Circumference} = 2 \pi r \]

- Given that the radius \( r = 100 \, \text{m} \):

\[ \text{Circumference} = 2 \times \pi \times 100 \, \text{m} \approx 2 \times 3.14 \times 100 \, \text{m} = 628 \, \text{m} \]

- Now, we can calculate the average speed:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{628 \, \text{m}}{62.8 \, \text{s}} = 10 \, \text{m/s} \]

3. **Final Results**:
- Average Velocity: \( 0 \, \text{m/s} \)
- Average Speed: \( 10 \, \text{m/s} \)

### Summary:
- The average velocity for each circular lap is \( 0 \, \text{m/s} \).
- The average speed for each circular lap is \( 10 \, \text{m/s} \).