Functions that connect location to time how complicated/accurate do they get

[Femme_physics]

So started up on calculus, I see there's a function that describe position with respect to time. P(t) = 40/3t^2

That seemingly simple formula provides all sorts of variation throughout it. I began to wonder, if any position with respect to time can be describe in a formula? I suppose that in the real world, things tend to be very complicated so these functions aren't very accurate. Let's say I'm trying to write a function to describe my position based on time as I jog in the park...isn't that in actuality impossible to do?

 

[zhermes]

If you're asking if you can be infinitely accurate... then of course you're correct: its not possible.
If you're asking if it can be done for all intents and purposes... then of course it can.

 

[Femme_physics]

Ah...just as I thought-- thanks :)

 

[sophiecentaur]

If you're asking if you can be infinitely accurate... then of course you're correct: its not possible.
If you're asking if it can be done for all intents and purposes... then of course it can.

Actually, you are ignoring the existence of chaotic motion, which is a very common phenomenon - not just a theoretical scenario. In chaotic motion, knowing the initial conditions to more and more accuracy doesn't determine the outcome with increasing accuracy. There will be chaotic influences even in a jog round the park.

 

[Femme_physics]

Actually, you are ignoring the existence of chaotic motion, which is a very common phenomenon - not just a theoretical scenario. In chaotic motion, knowing the initial conditions to more and more accuracy doesn't determine the outcome with increasing accuracy. There will be chaotic influences even in a jog round the park.

Aha! just as I suspected :)