To simulate a puck's movement, I use the following model (please restrain from discussing the model, it makes the simulation look the way I want it to) and would like to know how to calculate the total way the puck will move and how long it will take to do so.
My setup is: Per second, the puck looses 20% (=1-k) of its previous speed, so after a time t the speed will be v(t) = v(0) * k^t.
- If I look now at time t(n), how far has to puck traveled?
- How long will it travel until its speed falls below a defined v(min)?
- How far will it go until its speed drops below v(min)?
I have tried all kinds of formulas I remember from my physics lessons but I'm really stuck :-(