Deriving and Integrating Terminal Velocity Equation for Position

[Joza]

(dv_y)/(v_y+v_t) = (k/m)(dt) where v_y is y velocity, v_t is terminal velocity, k is fluid resistance constant, m is mass and t is time

This is my equation I derived for terminal velocity. I am going to integrate it for a function for position.

In my text, the limits of integration on the left side are written as V and 0. Right side is t and 0.

Could someone clear up the limits here? Like, there are 2 vs, v_y and v_t..what v is the limit referring to here? And I am a bit confused as to why the limits are needed here? I understand integration, but I am fairly new to it, maybe that's why!

 

[Hootenanny]

Integrating the differential you have there won't give to position as a function of time, it will give you velocity as a function of time.