Question

in free fall, when do we consider that the accelaration due to gravity is positive or negative?

Answer 1

when the direction of the object's movement is towards the earth its taken as positive because in the same direction acceleration due to gravity acts, but if its moving away or you can say up, then its taken as negative

Answer 2

Acceleration due to gravity is down (always).

So if axis is oriented upwards, then acceleration is negative.
If axis is oriented downwards, then acceleration is positive.

Of course you can choose orientation according to expected direction of motion, but sometimes bodies go up and come down again, so you have to make a decision and stick to it, then a single equation will determine the entire motion.

If you prefer to change axis when the body reaches the top of its trajectory, you can, but at the cost of writing 2 different equations for the apparent different phases of you motion.

Answer 3

Isn't positive acceleration associated with an increase in speed and negative associated with a decrease in speed?

Answer 4

No it is not. It can be, but it depends on the orientation of the axis.

In three dimension:

A motion is 'accelerated', i.e. increase in speed, when \(\vec a . \vec v >0\)
A motion is 'decelerated', i.e. decrease in speed, when \(\vec a . \vec v <0\)

Answer 5

Yes, I gave it some more thought, In fact the negative sign can be associated with only the direction like velocity and displacement. Deceleration occurs only when you have an initial velocity. It is acceleration in the opposite direction of motion. Its still a speeding up but in the opposite direction.