How can we understand acceleration direction (positive or negative)?

Question

I am studying motion in one dimension. I am having hard time to determine acceleration either positive or negative. How can I understand this?

For example in this question I thought accelaration was positive but it is negative so my answer was wrong.

A tennis ball is tossed upward with a speed of 3.0 m/s
​​We can ignore air resistance.
What is the velocity of the ball 0.40 s after the toss? 

t = 0.40 s

V0 = 3.0 m/s

v= ?

a= 9.81 m/s^2 but it should be -9.81 but why?

Answer 1

Once you fix the direction of the vertical axis, you fix the sign of the acceleration. In your example, you chose “up” to be positive since your velocity is $+3m/s$ for the ball going up. As gravity acts “down”, it means $g$ must be negative, i.e. $-9.8$.

The confusion occurs because in some problems it’s more convenient to define the vertical axis to point “down”.

Answer 2

You should first find the force acting on the ball. It's gravity of course.

Now, the acceleration of the ball is in the direction of the force (or, more exactly, in the direction of the net force. Here's gravity is the only force). As Newton's law states: $\mathbf{F} = m\mathbf{a}$, the direction of the acceleration and the net force is same.

Now take X-axis to be in the upward direction, Y-axis to the right. The velocity is directed in the positive X-direction and the force is in the negative X-direction. Hence, the body is accelerating downwards, and it is negative.

Note that negative acceleration means positive deceleration and vice-versa.

As gravity pulls the ball toward earth, it's velocity gradually decreases to zero at the top position of its trajectory. That means it's facing deceleration, or negative acceleration during its upward journey, and positive acceleration in the downward journey.

Answer 3

It depends what sign convection you choose, suppose you have chosen upward displacement as negative, then velocity and acceleration direction are different, hence you can take a=(+) , for basic problem remember if direction of velocity is opposite the force like gravity then by assigning upward displacement as positive, you can take a=(-) ,.