A lift is coming from `8th` floor and is just about to reach `4th` floor. Taking ground floor as origin and positive direction upwards for all quantities, which one of the following is correct ?

Options

A. x < 0, v < 0, a > 0
B. x > 0, v < 0, a < 0
C. x > 0, v < 0, a > 0
D. x > 0, v > 0, a > 0

Explanation

To solve the problem, we need to analyze the motion of the lift as it travels from the 8th floor to the 4th floor, taking the ground floor as the origin (0 position) and considering the positive direction to be upwards.

### Step-by-Step Solution:

1. **Identify the Positions**:
- Ground floor (0th floor) = 0
- 4th floor = 4
- 8th floor = 8

2. **Determine the Displacement (x)**:
- Displacement is calculated as:
\[ x = \text{final position} - \text{initial position} \]
- Here, the lift is moving from the 8th floor (initial position) to the 4th floor (final position):
\[ x = 4 - 8 = -4 \]
- Therefore, the displacement \( x < 0 \).

3. **Determine the Velocity (v)**:
- The velocity of the lift is in the direction of the displacement. Since the lift is moving downwards (from 8th to 4th floor), the velocity will also be negative:
\[ v < 0 \]

4. **Determine the Acceleration (a)**:
- As the lift approaches the 4th floor, it is about to stop. This means that the velocity of the lift is decreasing. Since the lift is moving downwards but slowing down, the acceleration must be in the opposite direction (upwards):
\[ a > 0 \]

5. **Summarize the Results**:
- Displacement \( x < 0 \)
- Velocity \( v < 0 \)
- Acceleration \( a > 0 \)

6. **Conclusion**:
- Based on the analysis, the correct option is that displacement is negative, velocity is negative, and acceleration is positive.