Hi, I'm an independent game developer (currently in college) and have been trying to solve a problem and get an equation for use within my physics engine. 1. The problem statement, all variables and given/known data Here's the problem/situation illustrated through two graphs and a diagram: http://i.imgur.com/qHAsU.jpg 2. Relevant equations unknown 3. The attempt at a solution Through the help of others in other forums I think we've solved the problem with force as it increases linearly with the following equation: t_2 = Log[(B + A d_2 + Sqrt[A d_2 (2 B + A d)])/B]))/Sqrt[A] It appears to give a reasonable answer although I have no way of double-checking it until it's implemented in the physics engine, however it does not work for decreasing linear force (you typically will get a negative within the squareroot). If you guys could help me out I'd be forever grateful. Thanks for your time and consideration!