The Force Diagram provided for the elevator rider shows a balance of forces: the up force and the down force are of equal strength. This will always be the case for an object with a constant velocity. But you need to determine what the Force Diagram looks like if the rider moves downwards and is slowing down. To do so, you will need to determine the direction of the acceleration. If the acceleration is upwards, then there must be more up force than down force. But if the acceleration is downwards, then there would be more down force than up force. Read on ...
The Direction of the Acceleration
The direction of an object's acceleration depends on two important features of the object's motion - the direction that the object is moving and whether the object is speeding up or slowing down.
The general rule is: If an object is slowing down, then the direction of the object's acceleration is the
opposite of the direction that the object is moving. On the other hand, if the object is speeding up, then the direction of the object's acceleration is the same as the direction that the object is moving.
Now apply this information to the elevator rider and determine the direction of its acceleration.
Beware of Misconceptions
A common misconception that a Physics student may have is to believe that forces are associated with the direction that an object is moving. That is, students falsely believe that an object that is moving downward must have more down force than up force. But we doubt that you've been taught that way ... at least not by a card-carrying Physics teacher. The fact is that forces are associated with accelerations or changes in the velocity. Forces don't cause objects to move in a given direction. Forces cause objects to change how they are moving in a given direction.
You want to determine the Force Diagram for an elevator rider that is moving downwards and is slowing down. You're probably paying attention to the moving downwards part ... but don't miss the slowing down part. The slowing down describes the change that is occuring. Forces when unbalanced cause objects to change the way they are moving. The rider was moving with a constant speed, When it changes to a slowing down motion, you must make sure there is more force against its motion than there is force in the direction of its motion.
But before you jump to an answer, make sure that you ... (read on).
Respect the Weight of the Situation
The down force is the force of gravity. This force depends on the rider's mass. Since the rider's mass is not changing, the force of gravity does not change. If you need a Force Diagram with less down force than up force, then make sure you accomplish this by increasing the up force since the down force (gravity) cannot be changed.
Inspect your answer options carefully to insure that the force of gravity in your selected answer is the same size as the force of gravity in the given Force Diagram. You should be able to rule out a few options just by inspecting this detail.