A racecar, traveling at constant speed, makes one lap around a circular track of radius r in a time t .
When the car has traveled halfway around the track, what is the magnitude of its displacement from the starting point ?

Options

A. r
B. 2r
C. `pi` r
D. `2 pi r`

Answer

To solve the problem, we need to determine the magnitude of the displacement of the racecar after it has traveled halfway around a circular track of radius \( r \).

### Step-by-Step Solution:

1. **Understanding the Circular Motion**:
The racecar is moving in a circular path with a radius \( r \). When it travels halfway around the track, it reaches the point directly opposite its starting point.

**Hint**: Visualize the circular track and mark the starting point and the point halfway around the circle.

2. **Identifying the Starting and Ending Points**:
Let’s denote the starting point of the racecar as point A. After traveling halfway around the circle, the car reaches point B, which is directly opposite point A on the circle.

**Hint**: Draw a diagram of the circle and label the points A (starting point) and B (halfway point).

3. **Understanding Displacement**:
Displacement is defined as the shortest distance from the initial position to the final position. In this case, the displacement is the straight line distance between points A and B.

**Hint**: Remember that displacement is not the same as distance traveled; it is the straight line connecting two points.

4. **Calculating the Displacement**:
The distance between points A and B is the diameter of the circle. The diameter \( D \) of a circle is given by the formula:
\[ D = 2r \]
where \( r \) is the radius of the circle.

**Hint**: Recall the relationship between the radius and diameter of a circle.

5. **Conclusion**:
Therefore, the magnitude of the displacement of the racecar from its starting point after traveling halfway around the track is:
\[ \text{Magnitude of Displacement} = 2r \]

### Final Answer:
The magnitude of the displacement from the starting point is \( 2r \).