An object when moves in the negative direction with a changing velocity. An object which moves in the negative direction has a negative velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion ( a positive acceleration).
For negative velocity: velocity of an object can be negative. This can be better explained with object in free space like aircraft. Aircraft's speed is measured relative to direction in which it is flying, its usually called airspeed. You might have seen in many modern fighter aircraft videos that's maneuvering, they fly straight up and then they fall vertically. During this vertical fall, aircraft is accelerating downwards & due to suction created in-front of pitot tube (Device used to measure airspeed) velocity measured is negative.