How do i find t?

Ill explain in detail whats going on...

...
I have a moving Object.
Object only moves left or right, along the horizontal plane.
There are two general forces affecting the Objects movement.

(1) OBJECTS PERSONAL MOVEMENT
- Objects personal movement direction and speed is represented by V ( + for right - for left, V represents pixels moved along the horizontal plane )
- Object also has an Initial Speed, Vi
- Object also has a Wind Speed, Vw ( + for right - for left, Vw represents additional pixels moved along the horizontal plane )

(2) WIND
- Wind direction and power is represented by W ( + for right - for left, W represents the increase of Vw each frame, W does not change durring the cource of a simulation )

(3)
Every Frame this happens:
- Object moves V + Vw number of pixels
- W is added to Vw
- V is multiplied by D ( decelleration, a number between 0 and 1 )

WHAT I WANT
I want to be able to predict how far the Object moves from its original position before its Total Speed ( V + Vw ) reaches a Target Speed ( Vt ).

So i have
Vi
D
Vw
W
Vt
T ( Time/ Frame Nr )

- All values except Time ( T ) and Wind Speed ( Vw ) are known.
- All values are potential floats, only T is integer.

It is worth mentioning that there is generaly only a solution to this when Objects Initial Speed ( Vi ) and Wind Power ( Vw ) work in opposite directions ( +Vi -Vw or -Vi +Vw ).

EDIT: This has eventually become too troubblesome, and im stuck with a mediocre unsatesfying solution for now, but still if anyone are able to solve such a problem that would be most welcome!