Choose the correct statement from the following:

Options

A. The magnitude of velocity of a particle is equal to its speed at that instant
B. The magnitude of the average velocity in an interval is equal to its average speed in that speed in that interval
C. It is possible to have a situation in which the speed in an interval is zero
D. It is possible to have a situation which the instantaneous speed of particle is always zero but the average speed is not zero

Answer

To solve the question, we need to analyze each statement provided and determine which one is correct.

### Step-by-Step Solution:

1. **Evaluate the First Statement**:
- The first statement claims that "the magnitude of velocity of a particle is equal to speed at that instant."
- **Explanation**: Velocity is a vector quantity that has both magnitude and direction, while speed is a scalar quantity that only has magnitude. The magnitude of velocity is indeed equal to speed.
- **Conclusion**: This statement is **correct**.

2. **Evaluate the Second Statement**:
- The second statement claims that "the magnitude of average velocity in an interval is equal to its average speed in that interval."
- **Explanation**: Average velocity is defined as the total displacement divided by the total time taken, while average speed is the total distance traveled divided by the total time taken. These two quantities can differ, especially if the motion involves changes in direction.
- **Conclusion**: This statement is **incorrect**.

3. **Evaluate the Third Statement**:
- The third statement claims that "it is possible to have a situation in which the speed in an interval is 0."
- **Explanation**: Speed is defined as the distance traveled over time. If no distance is traveled (i.e., the object is at rest), then the speed can indeed be 0 over that interval.
- **Conclusion**: This statement is **incorrect**.

4. **Evaluate the Fourth Statement**:
- The fourth statement claims that "it is possible to have a situation in which the instantaneous speed of a particle is always zero but the average speed is not zero."
- **Explanation**: If the instantaneous speed is always zero, it means the particle is not moving at all. Consequently, the average speed, which is based on total distance over time, must also be zero.
- **Conclusion**: This statement is **incorrect**.

### Final Conclusion:
After evaluating all the statements, the only correct statement is the first one: "the magnitude of velocity of a particle is equal to speed at that instant."

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