An object at the end of a rope is attached to the ceiling of an elevator. If the elevator is allowed to free-fall and hit the ground, at impact the tension of the rope is greater than if the elevator was standing still.

Why in the equation below, the acceleration is positive for $m\overrightarrow{a}$

$T-mg=ma$

Is this because to the object at the end of the rope, the elevator appears to be accelerating upward? Why is the acceleration not negative, since the elevator was free-falling?

Why in the equation below, the acceleration is positive for $m\overrightarrow{a}$

$T-mg=ma$

Is this because to the object at the end of the rope, the elevator appears to be accelerating upward? Why is the acceleration not negative, since the elevator was free-falling?