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 `10ms^(-1)`, speed `10ms^(-1)`
B. Velocity zero, speed `10ms^(-1)`
C. Velocity zero, speed zero
D. Velocity `10ms^(-1)` speed zero

Answer

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

### Step 1: Understand the Definitions
- **Average Speed** is defined as the total distance traveled divided by the total time taken.
- **Average Velocity** is defined as the total displacement divided by the total time taken.

### Step 2: Calculate the Distance Traveled
The car is running on a circular track with a radius of 10 meters. The distance traveled in one complete lap (circumference of the circle) can be calculated using the formula:
\[ \text{Distance} = 2\pi r \]
Substituting the radius:
\[ \text{Distance} = 2\pi \times 10 = 20\pi \text{ meters} \]

### Step 3: Calculate the Time Taken
The time taken to complete one lap is given as 6.28 seconds.

### Step 4: Calculate the Average Speed
Using the formula for average speed:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{20\pi}{6.28} \]
Since \( \pi \approx 3.14 \):
\[ \text{Average Speed} = \frac{20 \times 3.14}{6.28} = \frac{62.8}{6.28} = 10 \text{ m/s} \]

### Step 5: Calculate the Displacement
For one complete lap on a circular track, the initial and final positions are the same. Therefore, the displacement is:
\[ \text{Displacement} = 0 \text{ meters} \]

### Step 6: Calculate the Average Velocity
Using the formula for average velocity:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{0}{6.28} = 0 \text{ m/s} \]

### Final Answers
- **Average Speed**: 10 m/s
- **Average Velocity**: 0 m/s