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!

Parametric Equation Speed

  1. Feb 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Can someone please tell me how to get the average speed of a particle moving along a path represented by parametric equations? Is it [itex]\frac{1}{b-a}\int_{a}^{b}\sqrt{\frac{dx }{d t}^2 + \frac{d y}{d t}^2}[/itex]

    Isn't this the arc length formula?
  2. jcsd
  3. Feb 12, 2009 #2
    This is the arc length formula. The average value formula is Favg=(1/b-a)INT[f(x)dx]. It seems you combined two formulas.
  4. Feb 12, 2009 #3
    But if I wanted the speed of a particle moving with a parametric graph, woldn't everything under the radical be my speed function?
  5. Feb 12, 2009 #4
    Actually, you may be right. I think that might actually work.
  6. Feb 13, 2009 #5


    User Avatar
    Science Advisor
    Homework Helper

    No, no, no. The average speed is displacement over time. It has nothing to do with arc length. It's sqrt((x(b)-x(a))^2+(y(b)-y(a))^2)/(b-a) where a is the intiial time and b is the final time. Right?
  7. Feb 13, 2009 #6
    Couldn't you also do the average value of the absolute value of the velocity graph?
  8. Feb 13, 2009 #7


    User Avatar
    Science Advisor
    Homework Helper

    Yes, you could. In which case that would be correct. Distance travelled/time could also be considered an average speed. I was only thinking of the displacement/time definition.
  9. Feb 13, 2009 #8
    Alirght, thank you for the help.

    Also, is there any way to determine if a particle traveling on a parametric path is increasing in speed? I know I can determine if the x and y are accelerating, but I can I determine if the particle itself is increasing?

    What if it was accelearating in the x direction but decelerating in the y? Would the particle's speed be increasing or decreasing?
  10. Feb 13, 2009 #9


    User Avatar
    Science Advisor
    Homework Helper

    The 'speed' is sqrt((dx/dt)^2+(dy/dt)^2), isn't it? Just look at whether that quantity is increasing or decreasing.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Parametric Equation Speed
  1. Parametric equations (Replies: 1)

  2. Parametric Equations (Replies: 6)

  3. Parametric Equation (Replies: 3)

  4. Parametric equation (Replies: 10)