A racecar, traveling at constant speed, makes one lap around a circular track of radius r in a time t .
What is the average speed of the car for one complete lap ?

Options

A. `r/t`
B. `(pi r)/(t)`
C. `(2r)/(t)`
D. `(2 pi r)/(t)`

Answer

To solve the problem of finding the average speed of a racecar making one lap around a circular track of radius \( r \) in a time \( t \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Distance Traveled**:
The racecar travels around a circular track, which means it covers the circumference of the circle. The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius of the circular track.

2. **Determine the Time Taken**:
The time taken to complete one lap around the track is given as \( t \).

3. **Calculate Average Speed**:
Average speed is defined as the total distance traveled divided by the total time taken. Therefore, the average speed \( v_{avg} \) can be calculated using the formula:
\[ v_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} \]
Substituting the values we have:
\[ v_{avg} = \frac{C}{t} = \frac{2\pi r}{t} \]

4. **Final Expression**:
Thus, the average speed of the racecar for one complete lap is:
\[ v_{avg} = \frac{2\pi r}{t} \]