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

Options

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

Answer

To determine the magnitude of the average velocity of a racecar making one complete lap around a circular track of radius \( r \) in a time \( t \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Average Velocity**:
The average velocity is defined as the total displacement divided by the total time taken. Mathematically, it can be expressed as:
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} \]

2. **Identify the Initial and Final Positions**:
In this scenario, the racecar starts from a point (let's call it point A) and returns to the same point after completing one full lap around the circular track.

3. **Calculate the Total Displacement**:
Displacement is defined as the shortest distance between the initial and final positions. Since the car returns to its starting point (point A), the total displacement is:
\[ \text{Total Displacement} = 0 \]

4. **Determine the Total Time**:
The total time taken for one complete lap is given as \( t \).

5. **Calculate the Average Velocity**:
Substituting the values into the average velocity formula:
\[ \text{Average Velocity} = \frac{0}{t} = 0 \]

6. **Conclusion**:
Therefore, the magnitude of the average velocity of the car for one complete lap is:
\[ \text{Average Velocity} = 0 \]