How do I calculate final velocity from acceleration, displacement and inital velocity? How do I calculate the final velocity ($v_f$) given a known constant acceleration ($a$), a known inital and final position ($x_i$ and $x_f$), and a known inital velocity ($v_i$), where $v_i$ can be either positive or negative?
This concerns motion in one dimension.
 A: If you use the standard equations of motions then yes. You may substitute position, velocity or acceleration as negative and still get the right answer as long as you follow the sign convention.
A: The equation of motion for such situation is:
$$v_f^2 = v_i^2 + 2a(x_f-x_i)$$
Now for the concern you made in your comment:

All equations I've found assumes a positive inital velocity :-(

There are two things that I want to say:


*

*In the equation stated above you can see that direction of velocity (initial or final) has no use as they are squared.

*Generally in kinematics we use the positive direction for deriving the the kinematic equations because then the value which we get after solving the equation (with sign) tells us whether the true value is along our direction of assumption or not. You can use negative sing too but that might just complicate the situation (in many cases). 
A: $$ v_f^2=v_o^2+2a(x_f-x_i) $$
Final velocity squared is equal to initial velocity squared plus 2 times acceleration times change in position (delta x).
