Answered By Michael Z

yes it can. The postive and negative signs of acceleration indicate which direction the acceleration is being applied. To tell if a object is speeding up or slowing down you need to take a look at the effect of acceleration ie the velocity. So if velocity and acceleration are in the same direction (same signs) then it is speeding up and if they are opposite direction ( opposite signs) then the object is slowing down. 

Answered By Emily D

Yes!

If your current velocity and acceleration are in the same direction, you will go faster in that direction.

If your current velocity and acceleration are in opposite directions, you will go slower (until your velocity hits 0).

The graph I attached shows how this can happen. The red line is acceleration (2m/s) and the blue line is velocity and the green line is the speed.

Velocity - cares which direction you're going; this is the blue line. We'll say negative is to the left. So the object starts by moving at 4m/s left. Acceleration is pushing at 2m/s² right, so eventually, the object slows to 0m/s, then speeds up but now going to the right

Speed - doesn't care what direction you're going. 4m/s to the left is just 4m/s to the left. This is the green line, it shows how the object slows down at first and then speeds up once the object's acceleration and velocity are going Right

Acceleration - it's constant in this case, but also cares what direction you're going. This example is accelerating at 2m/s to the Right.