Zero Acceleration

  1. 1. The problem statement, all variables and given/known data
    Let c be a path in R^3 with zero acceleration. Prove that c is a straight line or a point.

    2. Relevant equations
    F(c(t)) = ma(t)
    a(t) = c''(t)

    3. The attempt at a solution
    so i know that since the acceleration is zero, the velocity must be constant, and when you integrate a constant, you get a straight line...but how to I prove mathematically that the velocity is constant, because you can't integrate 0dt, as far as I know?
  2. jcsd
  3. arildno

    arildno 11,265
    Science Advisor
    Homework Helper
    Gold Member

    The indefinite integral, i.e, the anti-derivative of 0 is, indeed, a constant; that is we have:
  4. oh ok, so if I integrate that again I get that c(t) = Ct + D, which fits the general equation for a line

    but then, does that also prove that c(t) could just be a single point?
  5. arildno

    arildno 11,265
    Science Advisor
    Homework Helper
    Gold Member

    Indeed, since big C could be..0!
  6. oh. duh!
  7. HallsofIvy

    HallsofIvy 41,265
    Staff Emeritus
    Science Advisor

    Damn, I hate mixed "physics" and "mathematics" problems! You or whoever set this problem, should know that a "path" DOES NOT HAVE an "acceleration". I expect this problem should be "find the equation of motion of a particle whose trajectory is a given path in R3 with acceleration 0. Show that the path is either a straight line or a point". Then you would begin with [itex]\vec{a}= d\vec{v}/dt=[/itex] and go from there.
    Last edited: Oct 22, 2007
  8. Gib Z

    Gib Z 3,347
    Homework Helper

    The easiest way would have been to recognise that acceleration is a vector quantity, it is affected both by direction or magnitude. No acceleration, no change in direction, which means constant gradient. Simple as that.
Know someone interested in this topic? Share this thead via email, Google+, Twitter, or Facebook

Have something to add?
Similar discussions for: Zero Acceleration