For velocity to be negative you must first define a positive direction. So if up is positive, and down is negative, a ball dropped would accelerate in the negative direction when released.
A racing car facing forwards on a track in reverse gear, with the gas pedal down will be moving backwards (negative velocity) and as time goes on will go backwards faster and faster (acceleration).
"Acceleration", is defined as "change in velocity". Increasing speed is positive acceleration, slowing down is negative velocity. So in this sense, "negative velocity" has no meaning.
One example acceleration is when you have a car and the velocity starts to get higher its accelerating. When your car is slowing down it has negative velocity
