Forgive me but I'm going to change your notation a bit, so that it's less confusing.

Let:

v = velocity,

V_i = initial velocity

V_t = target velocity

T = time to reach target velocity

X = distance traveled to reach target velocity

The equation of motion that you are describing is this:

From this we have . Hence the time to reach the target velocity is

The distance traveled in time T is:

Substituting the value for T we get:

Hope this helps!