What does it mean when the acceleration and velocity of an elevator remain the same for values > and < than 0?

The data seem to be describing an elevator as it goes up two floors, with a stop at the intermediate floor. It's not a continuous motion that you can write an overall equation for. From a stopped position, it accelerates upward (and the velocity increases), and then has to decelerate to stop at the next floor. It does the same thing again as it goes up another floor. While it is stopped between floors, there is no velocity and no acceleration. The velocity changes gradually when it is changing--it cannot change immediately from one value to another. There is not enough information about what happens at large values of time. The motion of an elevator follows a certain pattern as it moves from one floor to another (the velocity may go higher if it is moving several floors at once), but each movement is separate. There is no way for the velocity and acceleration to be constant unless the acceleration is zero. If the acceleration is constant and nonzero, the velocity will keep on increasing. If the velocity is constant, the acceleration must be zero.

You should not assume that velocity is constant because it has the same value for all those points. It cannot be constant, because constant velocity means acceleration is zero. For example, at some time between -2 and -1, velocity will not be 1, even though it is 1 at -2 and 1 at -1. It will be higher than 1 at some points between -2 and -1, since acceleration is positive at -2 and negative at -1. Visualize the graph of velocity vs. time. Acceleration is the slope. Between -2 and -1, there will be a "hill". It's not possible from the information you gave to conclusively determine the acceleration at other times. You said you solved for the numbers above. Maybe the information you need for the next part of the problem is in a previous part.

These data tables correspond to COMPLETELY different situations. ------------------------- in few words, what does it mean when the velocity and acceleration are constant and remain the same??? The only way this could be true is if acceleration is zero and remains zero. It would be a situation where your object of interest travels in a straight line at a constant speed.

You should not assume that velocity is constant because it has the same value for all those points. It cannot be constant, because constant velocity means acceleration is zero. For example, at some time between -2 and -1, velocity will not be 1, even though it is 1 at -2 and 1 at -1. It will be higher than 1 at some points between -2 and -1, since acceleration is positive at -2 and negative at -1. Visualize the graph of velocity vs. time. Acceleration is the slope. Between -2 and -1, there will be a "hill". It's not possible from the information you gave to conclusively determine the acceleration at other times. You said you solved for the numbers above. Maybe the information you need for the next part of the problem is in a previous part.

These data tables correspond to COMPLETELY different situations. ------------------------- in few words, what does it mean when the velocity and acceleration are constant and remain the same??? The only way this could be true is if acceleration is zero and remains zero. It would be a situation where your object of interest travels in a straight line at a constant speed.