Find a curve such that time travel is minimum

In summary, the conversation is about finding the curve y=f(x) that would allow a ball to travel from point A to point B in the shortest amount of time. The conversation also includes discussions about using Newton's Second Law and the brachistochrone, as well as solving for velocity and determining kinetic and potential energy. The solution involves finding the curve in terms of velocity and separating for ds/dt.
  • #1
ksuer
4
0

Homework Statement


[PLAIN]http://vctson.com/temp/curve.jpeg
Find the curve y = f(x) so that the ball travels from A to B in minimum time?

Thanks!
 
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  • #2
What have you worked out thus far? You have to show some effort.
 
  • #3
I tried at some point on the curve, the gravity force goes down, then use 2nd Newton law. Thus, P = ma = my''. But, P = mg. It does not seem right and I can't find the relation y and x.
 
  • #4
Any hint? Thanks!
 
  • #5
this is the brachistochrone, so what is you kinetic and potential energy?

solve in terms of v then separate for ds/dt.

ds = sqrt(dx^2 + dy^2)
 

1. How is it possible for a curve to minimize time travel?

The concept of minimizing time travel is purely theoretical and has not been proven to be possible in real life. It involves manipulating the fabric of space-time to create a path that allows for the shortest distance between two points in time.

2. Is there any real-life application for this concept?

At this point, there is no practical application for minimizing time travel. It is primarily a topic of interest in science fiction and theoretical physics.

3. Can you provide an example of a curve that would minimize time travel?

Unfortunately, since this concept is purely theoretical and has not been proven to be possible, there are no known examples of a curve that would minimize time travel.

4. Are there any potential consequences of minimizing time travel?

Since this concept is purely theoretical, it is impossible to predict any potential consequences of minimizing time travel. It is important to note that time travel itself has not been proven to be possible, so any potential consequences would also be purely hypothetical.

5. How does this concept relate to current theories of time travel?

Minimizing time travel is a relatively new concept and is not widely discussed in the scientific community. It is not currently incorporated in any existing theories of time travel, but it may be explored in future theories as the concept develops.

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