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

In summary, the conversation discusses the function P(t) = 40/3t^2 which describes position with respect to time and its variations. The question is raised if any position with respect to time can be described in a formula, to which it is stated that while it may not be infinitely accurate, it can be done for all intents and purposes. However, it is also noted that chaotic motion, which is a common phenomenon, can affect the accuracy of these formulas.
  • #1
Femme_physics
Gold Member
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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?
 
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  • #2
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.
 
  • #3
Ah...just as I thought-- thanks :)
 
  • #4
zhermes said:
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.
 
  • #5
sophiecentaur said:
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 :)
 

1. How do functions that connect location to time work?

Functions that connect location to time are mathematical representations of the relationship between a specific location and a specific time. These functions use variables such as latitude, longitude, and time to show how one changes in relation to the other.

2. What is the significance of these functions in scientific research?

Functions that connect location to time are crucial in scientific research as they help to analyze and understand the relationship between location and time. These functions can provide valuable information for various fields such as climate change, weather forecasting, and geological studies.

3. How complicated can these functions get?

Functions that connect location to time can get very complicated depending on the level of accuracy and complexity required. Some functions may involve multiple variables and complex equations, while others may be simpler and more straightforward. It ultimately depends on the specific research question and the data being analyzed.

4. How accurate are these functions?

The accuracy of functions that connect location to time varies depending on the data used and the complexity of the function. In general, these functions can be highly accurate if the data is collected and analyzed correctly. However, there may be some margin of error due to factors such as measurement errors or data limitations.

5. Are there any limitations to these functions?

Yes, there are limitations to functions that connect location to time. These functions rely on accurate and reliable data, and any errors or biases in the data can affect the accuracy of the function. Additionally, these functions may not be able to accurately predict extreme or rare events due to limitations in the data or the complexity of the function.

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