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Question

A particle moves along a closed trajectory.  Which of the following is always true?

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: Option C
## CONCEPT FRAMEWORK
**Primary Concept**: Average speed and average velocity
**Related Topics**: Displacement, Distance, Motion
**Prerequisites**: Understanding of distance, displacement, speed, and velocity.
## SOLUTION PATHWAY
**Given Information**:
*   The particle moves along a closed trajectory.
**Method & Steps**:
1.  **Understanding Closed Trajectory**: A closed trajectory means the particle returns to its starting point.
    Reasoning: This implies that the net displacement is zero, while the total distance traveled is non-zero.
2. **Average Velocity**: Average velocity is defined as the total displacement divided by the time taken. 
     Formula/Rule: Average velocity =  $\frac{	ext{Total displacement}}{	ext{Total time}}$
3. **Average Speed**: Average speed is defined as the total distance traveled divided by the time taken.
    Formula/Rule: Average speed = $\frac{	ext{Total distance}}{	ext{Total time}}$
4. **Analysis**: Since the total displacement is zero for a closed trajectory, the average velocity will always be zero. However, since the particle covers a non-zero distance, the average speed will be a positive non-zero value.
    Key Point:  Distance is always a non-negative value, while displacement can be zero.
5. **Final Step**: Conclude that average speed cannot be zero because the distance is not zero for a closed trajectory.
   Result: Average speed cannot be zero.
   Verification: This aligns with the definitions of average speed and velocity for closed path trajectories.
## OPTION ANALYSIS
[A] :x: Average speed is not zero for a closed trajectory; it is the total distance divided by the total time.
[B] :x: Average velocity is always zero for a closed trajectory because the final position is the same as the initial position, resulting in zero displacement.
[C] ✓: Average speed cannot be zero because the total distance is not zero for a closed path.
[D] :x: Average speed is not equal to the magnitude of average velocity. Average speed will have a non-zero positive value; average velocity will always be zero for a closed trajectory.
## LEARNING AIDS
**Common Mistakes**:
1.  **Confusion between distance and displacement**: Distance is the total path length; displacement is the change in position from the initial to the final point. For closed paths, displacement is zero, but distance is not.
   How to avoid: Remember the definition of each term.
2.  **Assuming average speed is zero for closed paths**: Average speed is based on total distance which is non-zero for closed trajectories.
   How to avoid: Understand that average speed is based on distance, not displacement.
**Quick Tips**:
1. **Closed trajectory implies zero displacement**: This is a key concept to quickly determine the average velocity.
2. **Average speed is always non-negative**: For any motion, the average speed will always be a positive value or zero, but for a closed path, it cannot be zero.

ABDUL JILANI BASHA · Answer

Average speed is zero.

ABDUL JILANI BASHA · Answer

Average velocity is zero.

ABDUL JILANI BASHA · Answer

The correct Option is "Average speed cannot be zero."

ABDUL JILANI BASHA · Answer

Average speed is equal to the magnitude of average velocity.

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