Hi Guys, I'm a programmer working on a hobby project (physics simulation), and came across this forum while looking for ideas related to a 1 dimensional motion problem I have. Hopefully someone can help me out (or at least point me in the right direction!). =) 1. The problem statement, all variables and given/known data An object starts at a known velocity, acceleration, and time (0). It ends at a known velocity, acceleration, and displacement (from start position). I want to find a constant delta acceleration and elapsed time that would satisfy the start and end conditions. For simplicity sake I'm assuming no external acceleration forces, etc, at this point. Known: initial velocity (vi) initial acceleration (ai) initial time (0) final velocity (vf) final acceleration (af) final displacement from start position (sf) Unknown: constant delta acceleration (c) elapsed time (t) additional required constraints? 2. Relevant equations af = ai + ct vf = vi + ait + 1/2ct2 sf = vit + 1/2ait2 + 1/6ct3 3. The attempt at a solution So after having done some reading I think I need to use calculus and start with the formulas above. It seems like I should be able to use basic algebra to solve for c and t at this point. However, I'm not sure if: (a) That would actually generate correct 'real world' results, and (b) What additional constraints I would have to consider to ensure the math doesn't break on some arbitrary set of inputs. For example, under what conditions would it be impossible to generate a constant delta acceleration/elapsed time combination that satisfies my start and end conditions? Thanks for any help/pointers in advance!