Hi Guys,(adsbygoogle = window.adsbygoogle || []).push({});

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 (v_{i})

initial acceleration (a_{i})

initial time (0)

final velocity (v_{f})

final acceleration (a_{f})

final displacement from start position (s_{f})

Unknown:

constant delta acceleration (c)

elapsed time (t)

additional required constraints?

2. Relevant equations

a_{f}= a_{i}+ ct

v_{f}= v_{i}+ a_{i}t + 1/2ct^{2}

s_{f}= v_{i}t + 1/2a_{i}t^{2}+ 1/6ct^{3}

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Variable acceleration problem

**Physics Forums | Science Articles, Homework Help, Discussion**