A car runs at constant speed on a circular track of radius 10m. taking 6.28s on each lap. The average speed and average velocity on each complete lap is:-

Options

A. Velocity `10" ms"^(–1)", speed 10 ms"^(–1)`
B. Velocity zero, speed `10" ms"^(–1)`
C. Velocity zero, speed zero
D. Velocity `10" ms"^(–1)`, speed zero

Answer

To solve the problem regarding the average speed and average velocity of a car running on a circular track, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Radius of the circular track, \( r = 10 \, \text{m} \)
- Time taken for one complete lap, \( t = 6.28 \, \text{s} \)

2. **Calculate the Circumference of the Circular Track:**
- The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
- Substituting the value of \( r \):
\[ C = 2 \pi (10) = 20 \pi \, \text{m} \]
- Using \( \pi \approx 3.14 \):
\[ C \approx 20 \times 3.14 = 62.8 \, \text{m} \]

3. **Calculate the Average Speed:**
- Average speed is defined as the total distance traveled divided by the total time taken:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{C}{t} \]
- Substituting the values:
\[ \text{Average Speed} = \frac{62.8 \, \text{m}}{6.28 \, \text{s}} = 10 \, \text{m/s} \]

4. **Calculate the Average Velocity:**
- Average velocity is defined as the total displacement divided by the total time taken. Since the car returns to its starting point after one complete lap, the displacement is zero:
\[ \text{Displacement} = 0 \, \text{m} \]
- Therefore, the average velocity is:
\[ \text{Average Velocity} = \frac{\text{Displacement}}{\text{Total Time}} = \frac{0 \, \text{m}}{6.28 \, \text{s}} = 0 \, \text{m/s} \]

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