Challanging Problem It is nessecary to solve quicly

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Discussion Overview

The discussion revolves around a problem involving the motion of a car along a real line, specifically focusing on the relationship between the car's maximum velocity and its acceleration at certain points during its trip. The problem requires proving a condition related to the car's velocity and acceleration, and participants are exploring the implications of the Mean Value Theorem in this context.

Discussion Character

  • Homework-related, Mathematical reasoning, Technical explanation

Main Points Raised

  • One participant presents a problem statement involving a car's motion, asking for verification of a condition related to maximum velocity.
  • Another participant suggests that the Mean Value Theorem can be used to show that the maximum velocity L is greater than 1.
  • A different participant claims that the Mean Value Theorem indicates L is greater than 0.
  • Further, a participant notes that the Mean Value Theorem implies the existence of a point c in the interval [0,1] where the derivative of the position function equals 1.
  • One participant expresses a desire for assistance in completing their solution.
  • Another participant inquires about the affiliation of the original poster, suggesting a possible connection to a university.

Areas of Agreement / Disagreement

Participants appear to agree that the Mean Value Theorem is relevant to the problem, but there is no consensus on the implications regarding the maximum velocity L, as different claims about its bounds (greater than 1 versus greater than 0) are presented.

Contextual Notes

The discussion does not resolve the mathematical steps necessary to prove the initial claim regarding L and the conditions under which the Mean Value Theorem applies.

vip89
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Challanging Problem " It is nessecary to solve quicly"

I have a problem :
A car moves along the real line from x = 0 at t = 0 to x = 1 at t = 1, with
differentiable position function x(t) and differentiable velocity function v(t) = x’(t).
The car
begins and ends the trip at a standstill; that is v = 0 at both the beginning and the end of
the trip. Let L be the maximum velocity attained during the trip. Prove that at some time
between the beginning and end of the trip, l v’ l > L^2/(L-1).

Can you verify that L > 1 ?

Thankx
 
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You can show L > 1 using the Mean Value Theorem
 
By mean value theorem I can find that L>0
 
The MVT would say that there exists c in t = [0,1] such that
f'(c) = (x(1) - x(0)) / (t1 - t0) = (1-0) / (1-0) = 1.
 
That is my solution
How I can compleat it??
 

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You are from UOS
right?
 

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