Calculate initial velocity to move a set distance with inertia

Question

I want to move something a set distance. However in my system there is inertia/drag/negative accelaration. I\'m using a simple calculation like this for it:

Answer 1

Distance travelled is just the integral of velocity with respect to time. You need to integrate your expression with respect to time with limits [v, 0] and this will give you an expression for distance in terms of v (initial velocity).