Does a negative acceleration always mean that the object is slowing down?

Sometimes, but definitely not always! Note: it's all dependent on which direction has been assigned '+'. Acceleration is a vector quantity, (the rate of change of velocity), meaning it has both magnitude and direction. Hence, if a 2D car on a plane was accelerating towards the left (i.e negative acceleration) and its velocity was also to the left too (negative), the car would speed up NOT slow down regardless of the negatives. The key to determining whether something is speeding up or slowing down is therefore looking at the directions of the velocity and acceleration vectors:1) Same direction - The body must "speed up", implying a '+' sign2) Opposite direction - The body must "slow down", implying a '-' sign3) At right angles to each other - The acceleration is "centripetal" and will vary regardless of constant linear velocity.