Final answer:
The weight of the person when the lift moves up with constant speed is the average of the apparent weights when moving up and down with acceleration, which is option (a) (w₁ + w₂) / 2.
Step-by-step explanation:
The apparent weight of a person inside a lift moving with an acceleration is different from when the lift is at a constant velocity. When the lift moves upwards with acceleration, the apparent weight w₁ includes the actual weight plus some additional force due to the acceleration of the lift. Conversely, when moving downwards with the same acceleration, the apparent weight w₂ is less because the acceleration reduces the normal force exerted by the scale.
However, when the lift moves up or down with a constant speed, there is no acceleration involved, meaning the apparent weight will be the actual weight of the person. At a constant velocity in any direction, the acceleration is zero, meaning the net force is zero and the only force registered by the scale would be the actual gravitational force acting on the person's mass.
Therefore, the weight of the person when the lift moves up with constant speed would be the average of w₁ and w₂, which is option (a) (w₁ + w₂) / 2, since this is the weight the person would have without any additional acceleration forces acting on them.