A woman in an elevator lets go of her briefcase, but it does not fall to the floor. How is the elevator moving?

The acceleration is described as the rate of the change of the velocity of an object with respect to the time taken by that object. Acceleration is described as a vector quantity and it consists of direction and also magnitude.

If the elevator was moving upward, then the briefcase would have fallen to the ground. Hence, the elevator is moving downward. The velocity of the briefcase and the woman is equal. The initial velocity of the briefcase that is relative to the woman is zero but the initial velocity of the briefcase that is relative to the observer standing in the ground is not the same as relative to the woman.

The velocity of the briefcase significantly increases as it goes closer to the ground as it is increased by the gravitational force. As the velocity of the briefcase relative to the woman remains stationary that shows the velocity of the elevator significantly increases as it goes closer to the ground.

Hence, the elevator’s and the briefcase’s acceleration is the same that is .$-9.8\hspace{0.33em}m/s^2$

Thus, the elevator is moving due to the gravitational acceleration.