1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof that v'(t) is orthogonal to v(t)

  1. Sep 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that if v(t) is any vector that depends on time, then v'(t) is orthogonal to v(t).

    Hint given: Consider the derivative of v^2.


    3. The attempt at a solution

    V'^2 = d/dt (v * v)
    = v d/dt + v d/dt
    = d/dt (v+v)
    = 2v d/dt

    ??
     
  2. jcsd
  3. Sep 19, 2012 #2
    For ANY vector that's not true. E.g., the displacement, velocity and acceleration vectors of a body falling from rest are all parallel.

    The statement is true for vectors whose magnitude is constant (but direction changes). Can you see the relevance of the hint given?
     
  4. Sep 19, 2012 #3

    Curious3141

    User Avatar
    Homework Helper

    Your notation is atrocious, frankly. What you wrote, [itex]{(v')}^2[/itex] represents the square of the derivative, not the derivative of the square.

    There are many other errors in the rest of the working as well. It's hard to tell if they represent typos or errors in thinking. Please use LaTex.

    What you're supposed to be focussing on is the time derivative of [itex]\overrightarrow{v}.\overrightarrow{v}[/itex], i.e. [itex]\frac{d}{dt}(\overrightarrow{v}.\overrightarrow{v})[/itex]. What happens when the velocity has a constant magnitude?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proof that v'(t) is orthogonal to v(t)
  1. How to get v(t)? (Replies: 2)

  2. V(t) and x(t) (Replies: 1)

Loading...