Before you ever start doing a problem that involves direction, YOU DECIDE which direction you're going to call positive.
If you call UP the positive direction, then the force of gravity is a negative force (it pulls down), the acceleration of gravity is a negative acceleration (because it's in the direction of a negative force), and things that are falling have negative velocity.
It's your decision.
The acceleration due to gravity and the force of gravity are in the same direction. If something falls out of your hand, OF COURSE it's going to move in the same direction as the force on it.
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Let's say you decided to call UP the positive direction. Then the acceleration of gravity, and the force of gravity, are both negative.
Now you throw a rock straight UP.
-- Its velocity is positive.
-- But its acceleration is negative, so its velocity is going to keep shrinking, less and less, until it becomes zero. (Top of the rock's trip.)
-- Since the negative acceleration points down, it eventually conquers the upward velocity, and the velocity begins to point down (negative).
-- Now the acceleration is in the same direction as the velocity (both are negative), so the velocity starts growing, becoming more and more negative, as the acceleration keeps adding speed to it.
What does all this mean ?
When you throw a rock straight up, it goes slower and slower, strops rising at some point, starts falling, then gets faster and faster as it falls.
Everybody knows this as soon as they get to be 2 or 3 years old. But they don't think about it in negative and positive velocity and acceleration, until they get to high school and learn the language of Physics.
