So I am doing some theoretical work with rockets and had a few question regarding acceleration and air resistance.

Vf ² = Vo ² + 2(A)(T)
Where Vf ² is the final velocity, Vo ² is the initial velocity, A is acceleration, and T is time.

Instead of just substituting a constant for (A), can a function relating (A) with respect to (T) be substituted?

no. These equations assume acceleration is constant. Your equation is wrong.

The equation V_f^2 - V_0^2 = 2ad comes from the following:


\displaystyle\int_{d_0}^{d_f} {a dx } = \int _{V_0}^{V_f} {v dv}


If a is constant, this becomes

2ad = V_f^2 - V_0^2


But if a is not constant, then the integral on the left hand side becomes more complicated:

2 \displaystyle\int_{d_0}^{d_f} {a(x) dx } = V_f^2 - V_0^2