Mark the correct statement

Options

A. magnitude of the velocity of a particle is equal to its speed
B. The magnitude of average velocity in an interval is equal to its average speed in that interval
C. is possible to have a situation in which the speed of a particle is always zero but the average speed is not zero
D. It is possible to have a situation in which the speed of the particle is never zero but the average speed in an interval is zero

Explanation

To solve the question, we need to evaluate the given statements about velocity and speed and determine which one is correct. Let's analyze each statement step by step:

### Step 1: Understanding Velocity and Speed
- **Velocity** is a vector quantity that has both magnitude and direction. It is defined as the rate of change of displacement with respect to time.
- **Speed** is a scalar quantity that only has magnitude. It is defined as the rate of change of distance with respect to time.

### Step 2: Evaluating Statement A
- **Statement A**: The magnitude of the velocity of a particle is equal to its speed.
- **Analysis**: The magnitude of the velocity vector is calculated as \( \sqrt{a^2 + b^2 + c^2} \), which is indeed equal to the speed (the total distance traveled per unit time). Therefore, this statement is **correct**.

### Step 3: Evaluating Statement B
- **Statement B**: The magnitude of the average velocity in an interval is equal to the average speed in that interval.
- **Analysis**: Average velocity is defined as displacement divided by time, while average speed is distance divided by time. Since displacement and distance can differ (e.g., in circular motion), this statement is **incorrect**.

### Step 4: Evaluating Statement C
- **Statement C**: It is possible to have a situation in which the speed of a particle is always 0 but the average speed is not 0.
- **Analysis**: If the speed is always 0, it means the particle is not moving, hence the average speed must also be 0. This statement is **incorrect**.

### Step 5: Evaluating Statement D
- **Statement D**: It is possible to have a situation in which the speed of a particle is never zero but the average speed in an interval is zero.
- **Analysis**: If the speed is never zero, the particle is always in motion, which means it will cover some distance. Therefore, the average speed cannot be zero. This statement is **incorrect**.

### Conclusion
After analyzing all the statements, we find that:
- **Correct Statement**: Statement A is correct, while Statements B, C, and D are incorrect.

### Final Answer
The correct statement is **A**: The magnitude of the velocity of a particle is equal to its speed.

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