A particle starts from the origin, goes along X-axis to the point (30m, 0) and then returns along the same line to the point (-30m,0). The displacement and distance of the particle during the trip are

Options

A. 0, 60m
B. 60m,30m
C. 90m, -30m
D. `-30m, 90m`

Explanation

To solve the problem, we need to determine both the displacement and the distance traveled by the particle during its trip. Let's break it down step by step.

### Step 1: Understand the motion of the particle
The particle starts at the origin (0, 0), moves to the point (30 m, 0), and then returns to the point (-30 m, 0).

### Step 2: Calculate the displacement
Displacement is defined as the shortest straight-line distance from the initial position to the final position, along with the direction.

- **Initial Position**: (0, 0)
- **Final Position**: (-30, 0)

Displacement can be calculated using the formula:
\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} \]

Substituting the values:
\[ \text{Displacement} = -30 \, \text{m} - 0 \, \text{m} = -30 \, \text{m} \]

### Step 3: Calculate the distance
Distance is the total length of the path traveled, regardless of direction.

1. The particle first travels from the origin to (30 m, 0), which is a distance of 30 m.
2. Then, it returns from (30 m, 0) to (-30 m, 0). This return journey is another 60 m (30 m to return back to the origin and then another 30 m to reach (-30 m, 0)).

Total distance traveled can be calculated as:
\[ \text{Total Distance} = \text{Distance to (30 m, 0)} + \text{Distance to (-30 m, 0)} \]
\[ \text{Total Distance} = 30 \, \text{m} + 60 \, \text{m} = 90 \, \text{m} \]

### Step 4: Summarize the results
- **Displacement**: -30 m
- **Total Distance**: 90 m

### Final Answer
- Displacement: -30 m
- Distance: 90 m