I don't think it is that simple...
If you have a tertiary substrate it will give SN1 no matter what the nucleophile..
Is it just in acetic acid, or is there also an acetate salt added? In pure acetic acid, the autoionization constant is 3.5 x 10-15, so there is 6 x 10-8 M acetate ions in pure acetic acid which is pretty low. So in pure acetic acid, acetic acid might be the nucleophile, but with some added acetate it is likely to be acetate ion.
What is the temperature? Refluxing acetic acid?
The classical physical organic chemists (Bartlett, Winstein, Olah, etc) undoubtedly answered all these questions as they argued about the norbornyl cation and so forth.