I haven't studied math in many years, so this might be trivial but I would appreciate any help nonetheless. I want to calculate the distance it takes for a vehicle to reach a specific speed. I have found this equation(Sorry for the Swedish):
It gives the acceleration at a specific speed based on air resistance, friction, incline and the power of the vehicle, etc.
How do I convert this to a function of speed and distance? I want the end result to look like this (x=distance, y=velocity, each line representing a different incline %):
I'm guessing I need to integrate, but I can't remember exactly how. Any help would be appreciated.