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 correctA 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 ?

The correct option is x < 0, v < 0, a > 0.

Let us analyze the sign of each physical quantity step-by-step based on the given coordinate system:

1. Velocity ($v$): The lift is moving downwards (descending from the 8th floor towards the 4th floor). Since the positive direction is defined as upwards, any downward motion must have a negative velocity. Thus, we have:
$v<0$

2. Acceleration ($a$): The lift is "just about to reach" the 4th floor, meaning it is slowing down (decelerating) to come to a stop. When an object is slowing down, its acceleration acts in the direction opposite to its velocity. Since the velocity is directed downwards (negative direction), the acceleration must be directed upwards (positive direction). Thus, we have:
$a>0$

3. Position ($x$): Based on the provided correct option, the coordinate of the position is:
$x<0$

Putting all these conditions together, we obtain the correct set of relations:
$x<0$, $v<0$, $a>0$