A particle starts from the origin, goes along x-axis to the point (10 m, 0) and then returns along. The same line to the point (-10 m, 0). The distance and displacement of the particle during the trip are

Options

A. 20 m, 0
B. 30 m, 10 m
C. 30 m, - 10 m
D. 20 m, 10 m

Answer

To solve the problem, we need to calculate the distance and displacement of a particle that moves along the x-axis from the origin to the point (10 m, 0) and then returns to the point (-10 m, 0).

### Step-by-Step Solution:

1. **Identify the Initial and Final Positions:**
- The particle starts at the origin, which is the point (0 m, 0).
- It first moves to the point (10 m, 0).
- Then, it returns to the point (-10 m, 0).

2. **Calculate the Displacement:**
- Displacement is defined as the shortest distance from the initial position to the final position, along with the direction.
- Initial position (O) = (0 m, 0)
- Final position (F) = (-10 m, 0)
- The displacement can be calculated as:
\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} = (-10 \, \text{m}) - (0 \, \text{m}) = -10 \, \text{m} \]
- The negative sign indicates that the displacement is in the negative x-direction.

3. **Calculate the Distance:**
- Distance is the total length of the path traveled by the particle.
- The particle travels from (0 m, 0) to (10 m, 0), which is a distance of 10 m.
- Then, it returns from (10 m, 0) to (-10 m, 0). The distance for this part of the journey is:
\[ \text{Distance} = 10 \, \text{m} + 10 \, \text{m} + 10 \, \text{m} = 30 \, \text{m} \]
- Therefore, the total distance traveled is 30 m.

4. **Final Results:**
- The displacement of the particle is -10 m.
- The distance traveled by the particle is 30 m.

### Conclusion:
- **Displacement:** -10 m
- **Distance:** 30 m