Under what conditions (s) is the magnitude of average velocity of an object equal to its average speed ?

Explanation

To determine the conditions under which the magnitude of average velocity of an object is equal to its average speed, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Definitions**:
- Average Velocity (V_avg) is defined as the total displacement divided by the total time taken:
\[ V_{avg} = \frac{\text{Displacement}}{\text{Time}} \]
- Average Speed (S_avg) is defined as the total distance traveled divided by the total time taken:
\[ S_{avg} = \frac{\text{Distance}}{\text{Time}} \]

2. **Identify the Relationship**:
- For the average velocity and average speed to be equal, we need:
\[ |V_{avg}| = S_{avg} \]
- This implies:
\[ \frac{\text{Displacement}}{\text{Time}} = \frac{\text{Distance}}{\text{Time}} \]
- Simplifying this gives:
\[ \text{Displacement} = \text{Distance} \]

3. **Conditions for Equality**:
- Displacement is equal to distance when the object moves in a straight line without changing direction. This means:
- The object must travel in a single direction.
- There should be no turns or changes in the path.

4. **Conclusion**:
- Therefore, the magnitude of average velocity is equal to the average speed when the object moves in a straight line in a single direction without changing its path.

### Summary:
The conditions under which the magnitude of average velocity equals average speed are:
- The object moves in a straight line.
- The object does not change direction.