Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Vector analysis question on acceleration

  1. Feb 21, 2009 #1
    1. The problem statement, all variables and given/known data

    A moving particle reaches its max. speed at the instant t = 3. (Before and after 3, its speed is less.) It follows that the particle's acceleration is 0 at the instant t = 3... Show that this is FALSE

    2. Relevant equations

    v = dR/dt
    a = d^2 R / dt^2

    3. The attempt at a solution

    How do I show this is false? The derivative of velocity is acceleration so I would think it's true and is indeed 0. This is on a chapter for vector analysis on acceleration and curvature.
  2. jcsd
  3. Feb 21, 2009 #2


    User Avatar
    Homework Helper
    Gold Member

    If the particle's acceleration were 0 at t=3, why would it slow down?:wink:
  4. Feb 21, 2009 #3
    But the acceleration has to be 0 because at this point the speed is maximum... so on one side there should be negative acceleration and on the other side positive.
  5. Feb 21, 2009 #4


    User Avatar
    Homework Helper
    Gold Member

    No, if the acceleration at t=3 were zero, then if you measured the speed of the particle a very short time later it would be unchanged.

    It's true that [tex]\frac{d}{dt} ||\vec{v}||=0[/tex] at t=3, but that doesn't necessarily mean [tex]||\vec{a}||=0[/tex] at t=3.

    This rests on the fact that [tex]\vec{v}[/tex] is a vector, it has both magnitude and direction and just because its magnitude isn't changing doesn't mean it's direction can't be changing. If it's direction is changing, then [tex]\vec{a}=\frac{d\vec{v}}{dt}\neq0[/tex] :wink:

    There is an expression for [itex]\vec{a}[/itex] in terms of its tangential and normal components that you should know (it involves curvature), use that to prove that the acceleration is non-zero at t=3!:smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook