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 analyze the statements provided and determine which one is correct. Let's break it down step by step.

### Step 1: Analyze Statement A
**Statement A:** "Magnitude of velocity of a particle is equal to its speed."

- **Explanation:**
- Velocity is a vector quantity, which means it has both magnitude and direction. The magnitude of velocity is simply the speed of the particle.
- Mathematically, if the velocity vector is represented as \( \vec{v} = a \hat{i} + b \hat{j} + c \hat{k} \), then the magnitude of the velocity is given by:
\[ |\vec{v}| = \sqrt{a^2 + b^2 + c^2} \]
- Speed, on the other hand, is defined as the magnitude of the velocity vector. Therefore, the statement is true.

### Step 2: Analyze Statement B
**Statement B:** "The magnitude of average velocity in an interval equals its average speed in that interval."

- **Explanation:**
- Average velocity is defined as the total displacement divided by the total time taken.
- Average speed is defined as the total distance traveled divided by the total time taken.
- In general, the total displacement (which is a straight line from the start to the end point) is less than or equal to the total distance traveled (which accounts for the entire path taken). Therefore, the magnitude of average velocity can be less than average speed.
- Thus, this statement is false.

### Step 3: Analyze 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."

- **Explanation:**
- If the speed of a particle is always 0, it means the particle is not moving at all. Therefore, the average speed, which is calculated over a time interval, must also be 0.
- This statement is false because if speed is zero at all times, the average speed cannot be anything other than zero.

### Step 4: Conclusion
After analyzing all three statements:

- Statement A is **true**.
- Statement B is **false**.
- Statement C is **false**.

Thus, the correct answer is **Statement A**.