A car runs on a circular track at a constant speed. The circular track has a radius of 100m. If the car takes 62.8 on each lap, its average speed is

Options

A. `20ms^(-1)`
B. `10ms^(-1)`
C. `5ms^(-1)`
D. zero

Answer

To find the average speed of the car running on a circular track, we can follow these steps:

### Step 1: Understand the problem
We need to calculate the average speed of a car that runs on a circular track with a radius of 100 meters, completing one lap in 62.8 seconds.

### Step 2: Calculate the circumference of the circular track
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.

Given:
- Radius \( r = 100 \) meters

Substituting the value of \( r \):
\[ C = 2 \pi \times 100 \]
\[ C = 200 \pi \text{ meters} \]

### Step 3: Calculate the average speed
The average speed \( v \) is defined as the total distance traveled divided by the total time taken. In this case, the total distance is the circumference of the track, and the total time is the time taken to complete one lap.

Using the formula:
\[ v = \frac{\text{Total Distance}}{\text{Total Time}} \]

Substituting the values:
\[ v = \frac{200 \pi}{62.8} \]

### Step 4: Calculate the numerical value
Using \( \pi \approx 3.14 \):
\[ v = \frac{200 \times 3.14}{62.8} \]
\[ v = \frac{628}{62.8} \]
\[ v = 10 \text{ m/s} \]

### Conclusion
The average speed of the car is \( 10 \text{ m/s} \).

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