How to calculate travel time as a function of distance

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Discussion Overview

The discussion revolves around calculating travel time as a function of distance using the drag equation. Participants explore the integration of motion equations under the influence of drag, addressing both theoretical and practical aspects of the problem.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant seeks assistance with calculating travel time using the drag equation but expresses difficulty with integrals.
  • Another participant suggests writing the equation of motion and integrating it, emphasizing the importance of establishing the equation before integration.
  • A third participant notes that the travel time as a function of position can be represented as an inverse function, but highlights that this may not always be single-valued in certain trajectories.
  • Some participants assert that the problem is solvable only through direct integration, implying that a lack of integration skills limits the ability to find a solution.
  • There is a discussion about the appropriateness of seeking direct solutions versus understanding the problem-solving process, with some participants expressing concern over "spoon feeding" solutions.

Areas of Agreement / Disagreement

Participants express differing views on the approach to solving the problem, with some emphasizing the necessity of integration while others challenge the notion of providing direct solutions. There is no consensus on how to best support the original poster's request.

Contextual Notes

Participants acknowledge limitations related to integration skills and the implications for solving the problem, but do not resolve these issues.

Who May Find This Useful

This discussion may be useful for individuals interested in the application of drag equations in physics, particularly those grappling with integration in the context of motion and travel time calculations.

Christofer Br
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I need help calculating travel time as a function of distance using drag equation: F_drag = crossection area * density * ballistic coefficient * 0.5 * v^2. Not posted in homework cause it's not, and I don't know how to solve integrals so I could not fill solution attempt box
 
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If drag is the only force acting, just write the equation of motion and integrate it. At least get the equation of motion before worrying about how to integrate.
 
If the trajectory of an object in 1D is ##x(t)##, then the travel time as function of position is just its inverse function ##t(x)##. In some cases this isn't single valued, though, as you can see in the case of a harmonic oscillator trajectory ##x(t) = A\sin \omega t##.
 
Christofer Br said:
I don't know how to solve integrals so I could not fill solution attempt box

This problem is solvable by direct integration, but if you do not know how to integrate, then the solution is simply beyond your capabilities. I do not think that there is any other way to deal with the problem, other than by integration.
 
Dr.D said:
This problem is solvable by direct integration, but if you do not know how to integrate, then the solution is simply beyond your capabilities. I do not think that there is any other way to deal with the problem, other than by integration.
I realized that from beginning, I am essentialy asking to be spoon fed a solution - certainly other people will stumble upon it too, I think it's overall a good contribution to the forum
 
My understanding is that PF is not about spoon feeding problem solutions. Good luck with your search.
 
Christofer Br said:
realised that from beginning, I am essentialy asking to be spoon fed a solution
That is absolutely not what we do here at Physics Forums.

Dr.D said:
This problem is solvable by direct integration, but if you do not know how to integrate, then the solution is simply beyond your capabilities.
I agree.
 

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