Question

A lift is coming from the 8th floor and is just about to reach the 4th floor. Taking ground floor as origin and positive direction upwards for all quantities, which one of the following is correct?
A. \[x < 0,v < 0,a > 0\]
B. \[x > 0,v < 0,a < 0\]
C. \[x > 0,v < 0,a > 0\]
D. \[x > 0,v > 0,a < 0\]

Answer 1

Hint: Consider the upward direction as positive direction and downward direction as negative direction. Hence, determine the direction of displacement of the lift. The velocity has the same direction as that of the displacement. Determine whether the motion of the lift is accelerating or retarding and determine the value of acceleration of the lift from value of its velocity.

Complete answer:
We have given that the lift is coming from the 8th floor and is about to reach the 4th floor.We have asked to determine that the displacement, velocity and acceleration of the lift are either positive of negative.It is given that the ground floor of the building is the origin and all the quantities in the upward direction are considered positive and the quantities in the downward direction are considered negative.

Since the lift is coming from the 8th floor to the 4th floor, the displacement of the lift is in the downward direction. Hence, the displacement of the lift is negative or less than zero.
\[x < 0\]
This shows that the option A is correct. But let us check the values of the velocity and acceleration of the lift.
Since the displacement of the lift is negative, the velocity of the lift must also be negative.
\[v < 0\]
We have given that the lift is about to reach the 4th floor. This means that the lift will stop when it reaches the 4th floor. This shows that the motion of the lift is retarding motion.
We know that in the retarding motion, if the velocity is negative then the acceleration is positive. Hence, the acceleration of the lift is positive.
\[a > 0\]
Therefore, the values of displacement, velocity and acceleration of lift are \[x < 0,v < 0,a > 0\].

Hence, the correct option is A.

Note:The students may think that the direction of the acceleration of lift is the same as that of the velocity in the downward direction. But the students should keep in mind that the direction of acceleration and velocity are the same in accelerating motion and opposite in the retarding motion. Hence, one should be careful while determining the direction of acceleration.