A car runs at a constant speed on a circular track of radius 100m, taking 62.8s for every circular loop. The average velocity and average speed for each circular loop respectively is:

Options

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

Explanation

To solve the problem, we need to find both the average speed and the average velocity of a car running on a circular track. Let's break it down step by step.

### Step 1: Calculate the Circumference of the Circular Track
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle. Given that the radius \( r = 100 \) m, we can calculate the circumference.

\[ C = 2 \pi \times 100 = 200\pi \text{ m} \]

### Step 2: Calculate the Average Speed
Average speed is defined as the total distance traveled divided by the total time taken. The total distance for one complete loop around the circular track is the circumference we just calculated, and the total time taken is given as 62.8 seconds.

Using the formula for average speed:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{200\pi}{62.8} \]

Calculating this:
\[ \text{Average Speed} \approx \frac{628.32}{62.8} \approx 10 \text{ m/s} \]

### Step 3: Calculate the 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 returns to the starting point after one complete loop, the displacement is zero.

Using the formula for average velocity:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{0}{62.8} = 0 \text{ m/s} \]

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