Average Velocity and Constant Acceleration

No, because it isn't valid only for constant acceleration. There are other velocity functions that also yield this average velocity.

 

It's posible for V_av=(V_i+V_f)/2 to be true for variable acceleration as well. Start off with a graph of velocity (y axis) versus time (x axis). Then the area below the horizontal line that goes from {t₀, V_av} to {t₁, V_av} = V_av x (t₁ - t₀) = the distance traveled. Then note that any line of any shape with the same amount of area under the line from {t₀, V_i} to {t₁, V_f} would also have the same average velocity as constant acceleration.