Without friction it is simple, because velocity changes linearly over time, so I can multiply average velocity with $timeDelta$. $$ velocity_{next} = velocity + acceleration * timeDelta $$ $$ position_{next} = position + \frac{velocity + velocity_{next}}{ 2} * timeDelta$$
Few formulas about my understanding of friction. If I'm wrong please tell me it :)
$$acceleration = 0$$ $$velocity_{next} = velocity * friction^{timeDelta}$$ $$velocity_0 = 8, \quad friction=0.5$$ $$velocity_1 = 4$$ $$velocity_2 = 2$$ $$velocity_3 = 1$$ $$velocity_4 = 0.5$$
Now I want to put velocity, acceleration and friction together, but it's hard for me, because velocity change by friction is exponential over time.