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Grumple
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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!). =)
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?
af = ai + ct
vf = vi + ait + 1/2ct2
sf = vit + 1/2ait2 + 1/6ct3
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!
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!). =)
Homework Statement
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?
Homework Equations
af = ai + ct
vf = vi + ait + 1/2ct2
sf = vit + 1/2ait2 + 1/6ct3
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!