Challanging Problem It is nessecary to solve quicly

  • Thread starter vip89
  • Start date
In summary, the conversation discusses a challenge of proving that at some point during a car's trip, the absolute value of its velocity function is greater than L^2/(L-1). The Mean Value Theorem is mentioned as a possible way to prove that L is greater than 1. The conversation ends with a question about completing the solution and confirming if the speaker is from UOS.
  • #1
vip89
32
0
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
 
Physics news on Phys.org
  • #2
You can show L > 1 using the Mean Value Theorem
 
  • #3
By mean value theorem I can find that L>0
 
  • #4
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.
 
  • #5
That is my solution
How I can compleat it??
 

Attachments

  • pass7.JPG
    pass7.JPG
    45.9 KB · Views: 420
  • pass8.JPG
    pass8.JPG
    36.9 KB · Views: 400
  • pass9.JPG
    pass9.JPG
    36.1 KB · Views: 358
  • #6
You are from UOS
right?
 

What is a challenging problem?

A challenging problem is a complex issue or situation that requires a significant amount of effort, resources, and critical thinking to solve. It often involves multiple factors and obstacles that make it difficult to find a straightforward solution.

Why is it necessary to solve challenging problems quickly?

Solving challenging problems quickly is important because it allows for timely and effective solutions to be implemented. Delaying the resolution of a challenging problem can lead to further complications and negative consequences, making it harder to solve in the long run.

How can one approach a challenging problem?

Approaching a challenging problem requires a systematic and analytical approach. This may involve breaking down the problem into smaller, more manageable parts, gathering relevant information and data, and considering all possible solutions before making a decision.

What skills are necessary to effectively solve challenging problems?

To effectively solve challenging problems, one needs strong analytical and critical thinking skills, as well as the ability to think creatively and outside the box. Effective communication, teamwork, and adaptability are also important in navigating and solving complex problems.

What are some common strategies for solving challenging problems?

Some common strategies for solving challenging problems include brainstorming and generating new ideas, seeking input and advice from others, conducting research and analysis, and testing and evaluating possible solutions. It is also important to remain flexible and open to alternative approaches when attempting to solve a challenging problem.

Similar threads

I Some questions on l'Hôpital rules
    • Calculus
Replies
9
Views
2K
I Displacement vs time under a time varying speed limit
    • Calculus
Replies
7
Views
868
I Multivariable fundamental calculus theorem in Wald
    • Calculus
Replies
2
Views
1K
A On uniform boundedness of the GD algorithm
    • Calculus
Replies
2
Views
1K
How to get general solution via Green's function?
    • Calculus and Beyond Homework Help
Replies
1
Views
703
B Riemann integrability of functions with countably infinitely many dis-
    • Calculus
Replies
3
Views
1K
Challanging Problem It is nessecary to solve quicly
    • Precalculus Mathematics Homework Help
Replies
12
Views
3K
I Verifying properties of Green's function
    • Differential Equations
Replies
1
Views
748
Null space of dual map of T = annihilator of range T
    • Calculus and Beyond Homework Help
Replies
0
Views
449
Graphing the Superposition of Two Standing Waves
    • Introductory Physics Homework Help
Replies
8
Views
566

Hot Threads

Recent Insights

Back
Top