Why Was the Acceleration Positive in Circular Motion?

[isukatphysics69]

Homework Statement

In picture, i already solved this problem but i had a question about the bottom question..
So i solved for the acceleration and remember that i got a negative value, i then reasoned with the question and put positive value and was correct.. but then i started thinking about it and realized that i would have thought that it was negative.. So now i am wondering why the acceleration was positive at that position?
if you think about this the ball is swinging and on its way down to the bottom of the swing so it should be speeding up right? so i got a negative acceleration value and so to me it makes sense that the velocity would be negative as it was swinging downward and since it was speeding up on the downward path the acceleration being negative makes sense... Can someone please clarify this?

Homework Equations

The Attempt at a Solution

Already done

 

[Orodruin]

Being positive or negative depends on how you have defined the directions. In the question they are asking for the rate of change of the speed, which implicitly defines a positive direction for you. If you are using any other definition of directions, you may get a different sign.

 

[isukatphysics69]

Being positive or negative depends on how you have defined the directions. In the question they are asking for the rate of change of the speed, which implicitly defines a positive direction for you. If you are using any other definition of directions, you may get a different sign.

I see, thank you!