- Does a negative acceleration mean an object is slowing down?
- Does a negative velocity basically mean you are moving at an opposite direction? The sign is just direction?
Think of a position axis $x$ starting at zero, positive to the right and negative to the left.
It is like a number line.
A positive velocity means that the value of $x$ is increasing eg going from $x=+3$ to $x=+5$ or $x=-7$ to $x=-4$ or $x = -3$ to $x=+4$.
A negative velocity means that the value of $x$ is decreasing eg going from $x=-3$ to $x=-5$ or $x=+7$ to $x=+4$ or $x = +3$ to $x=-4$.
A positive acceleration mean that a velocity is becoming more positive (or less negative) eg going from $v=+3$ m/s to $v=+5$ m/s or $v=-7$ m/s to $v=-4$ m/s or $v = -3$ m/s to $v=+4$ m/s.
A negative acceleration mean that a velocity is becoming more negative (or less positive) eg going from $v =-3$ m/s to $v =-5$ m/s or $v =+7$ m/s to $v =+4$ m/s or $v = +3$ m/s to $v =-4$ m/s.
well you have given answer in your own question! Velocity and acceleration are both vector quantities, meaning they have magnitude and 'direction'. The sign (+/-) will depend on the direction. To simplify, let me give you an easy example.. Case 1: An object is moving down from the top of a mountain. The acceleration (in this case 'g') will act in the direction of motion, hence called as 'positive acceleration'. Case 2: Same object is moving up. The acceleration (g) will act in the opposite direction of motion, hence called as 'negative acceleration'.
The same logic is behind negative velocity.
For more information, go to Wikipedia page.