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

Kinematics - how do u find distance travelled

  1. Jul 25, 2006 #1
    ok. so i have x(t) = something and v(t) = something

    i know x will give me the displacement for a set time

    say if i wanted the distance travelled in the first ten seconds, i know i can use the definite integral of velocity.

    Is there any easier way? like using the displacement equation?
  2. jcsd
  3. Jul 25, 2006 #2


    User Avatar
    Science Advisor

    Actually you can't use the definite integral of velocity-you have to use the definite integral of the absolute value of velocity or else you'd be measuring displacement and not distance. You don't want the distance travelled to start decreasing just because the velocity becomes negative.

    Since it is in 1 dimension, if it never turns around, then its distance travelled after 10 seconds is the absolute value of its position after 10 seconds. If it does turn around and double back on its path then what can you say about the distance?
  4. Jul 25, 2006 #3
    then it would be double!

    lol ok... so if i have like a parabola graph of displacement/time i can just add up from the y values of start to max/mins and end point etc.
  5. Jul 25, 2006 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    As orthodontist said, you must use the integral of the modulus of your function of velocity;

    [tex]\int^{10}_{0} \left| v(t) \right| dt [/tex]

    The process is quite laborious and not one of my favourite things to do, have you solved modulus functions before?
    Yes, that would work :smile: (I think)
  6. Jul 25, 2006 #5
    sweet thanks guys
    yeah ive done modulus functions
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook