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Vector Proof Of Constant Speed Means Perpendicular Acceleration.

  1. Jan 28, 2013 #1
    1. The problem statement, all variables and given/known data

    Prove that when speed is constant that V(T), and A(T) are perpendicular.

    2. Relevant equations

    I know this involves the dot product to show that the dot product of the vectors is zero.


    3. The attempt at a solution

    In my head I thought that since the speed is constant that there must be no acceleration. When I dot the zero acceleration vector to the velocity vector it is zero, but I am thinking that there is no way this can be right.
     
  2. jcsd
  3. Jan 28, 2013 #2
    What is "speed"? I'm guessing V and A are vectors
     
  4. Jan 28, 2013 #3

    Mark44

    Staff: Mentor

    How does speed relate to velocity? Your book should give a definition for speed.
     
  5. Jan 28, 2013 #4

    LCKurtz

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    That isn't true. For example, in uniform circular motion the speed is constant but the acceleration is nonzero towards the center. Think about differentiating ##\vec V\cdot \vec V##.
     
  6. Jan 28, 2013 #5
    How do you differentiate v dot v?
     
  7. Jan 28, 2013 #6

    ehild

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    It is a product. How do you differentiate a product?

    ehild
     
  8. Jan 28, 2013 #7
    Oh well duh that makes sense.
     
  9. Jan 28, 2013 #8

    LCKurtz

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    Of course, you first have to prove that the product rule works for dot products of vectors.
     
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