A particle is constrained to move on a straight line path. It returns to the starting point after 10 sec . The total distance covered by the particle during this time is 30 m . Which of the following statements about the motion of the particle is false

Options

A. Displacement of the particle is zero
B. Average speed of the particle is `3 ms^(-1)`
C. Displacement of the particle 30 m
D. Both (a) and (b)

Explanation

To solve the problem, we need to analyze the motion of the particle based on the information provided.

### Given Information:
- The particle returns to the starting point after 10 seconds.
- The total distance covered by the particle during this time is 30 meters.

### Step-by-Step Solution:

1. **Understanding Displacement**:
- Displacement is defined as the change in position of an object. It is a vector quantity and is calculated as the final position minus the initial position.
- Since the particle returns to its starting point, the initial and final positions are the same. Therefore, the displacement of the particle is:
\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} = 0 \, \text{m} \]

2. **Calculating Average Speed**:
- Average speed is defined as the total distance traveled divided by the total time taken.
- The total distance covered by the particle is given as 30 meters, and the total time taken is 10 seconds. Thus, the average speed can be calculated as follows:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{30 \, \text{m}}{10 \, \text{s}} = 3 \, \text{m/s} \]

3. **Analyzing Statements**:
- Now we need to evaluate the statements provided in the question:
- **Statement A**: Displacement of the particle is zero. (True)
- **Statement B**: Average speed of the particle is 3 m/s. (True)
- **Statement C**: The particle moved in a straight line. (True, as it is constrained to move on a straight line path)
- **Statement D**: The total distance covered is equal to the displacement. (False, since total distance is 30 m and displacement is 0 m)

4. **Conclusion**:
- The false statement among the options is that the total distance covered is equal to the displacement. Therefore, the correct answer is that the false statement is D.