During a accelerated motion of a particle

Options

A. average velocity of the particle is always less than its final velocity
B. average velociyt of the particle is always greater than its final velocity
C. average velocity of the particle may be zero also
D. average velocity of the particle is half its final velocity

Answer

To solve the question regarding the average velocity of a particle during accelerated motion, we will analyze the given statements step by step.

### Step-by-Step Solution:

1. **Understanding Average Velocity**:
The average velocity (V_avg) of a particle is defined as the total displacement (s) divided by the total time (t) taken. Mathematically, it can be expressed as:
\[ V_{avg} = \frac{s}{t} \]

2. **Displacement in Accelerated Motion**:
For a particle undergoing accelerated motion, the displacement can be calculated using the formula:
\[ s = ut + \frac{1}{2} a t^2 \]
where \( u \) is the initial velocity, \( a \) is the acceleration, and \( t \) is the time.

3. **Considering the Case When Motion Starts from Rest**:
If the motion starts from rest, then \( u = 0 \). Thus, the displacement simplifies to:
\[ s = \frac{1}{2} a t^2 \]

4. **Final Velocity in Accelerated Motion**:
The final velocity (v) of the particle can be calculated using the formula:
\[ v = u + at \]
Again, if the motion starts from rest (\( u = 0 \)), this simplifies to:
\[ v = at \]

5. **Calculating Average Velocity**:
Now substituting the expressions for displacement and time into the average velocity formula:
\[ V_{avg} = \frac{s}{t} = \frac{\frac{1}{2} a t^2}{t} = \frac{1}{2} a t \]
Since \( v = at \), we can express average velocity as:
\[ V_{avg} = \frac{1}{2} v \]

6. **Analyzing the Statements**:
- **Statement 1**: Average velocity of the particle is always less than its final velocity.
- This is true since \( V_{avg} = \frac{1}{2} v \).
- **Statement 2**: Average velocity of the particle is always greater than its final velocity.
- This is false.
- **Statement 3**: Average velocity of the particle may be 0.
- This is false in the context of accelerated motion starting from rest.
- **Statement 4**: Average velocity of the particle is half of its final velocity.
- This is true when the motion starts from rest, but not necessarily true for all cases.

7. **Conclusion**:
The correct statement is that the average velocity of the particle is always less than its final velocity.

### Final Answer:
The correct option is: **Average velocity of the particle is always less than its final velocity.**