Is it possible for an object that has a constant negative acceleration to change the direction in which it is moving.

Of course! If you call "up" the "positive" direction, then that's exactly

what happens every time you toss a stone or a ball up into the air.

The stone or the ball starts out with upward (positive) velocity. But the

acceleration of gravity is downward (negative). The effect on the ball is

that its positive velocity becomes smaller and smaller, eventually reaches

zero, and then becomes negative when the ball or the stone starts moving

downward.

It is possible.

Consider an object that is moving forward. If it gets a constant negative acceleration, then its speed will decrease. When it becomes negative, the object will move backwards : it will have changed its direction.