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

I Integrating Velocity

  1. Jan 11, 2019 #1

    opus

    User Avatar
    Gold Member

    Please see the attached image which are of my notes. In integrating acceleration, I have no confusions. But I have a specific question about integrating velocity.

    When we integrate velocity, do we get the displacement of ##x##, or do we get it's position at a certain time?
    I want to say it's the displacement as it's directly in the definition in green and integration is basically accumulated area. But I want to be sure.
    Thank you.
     

    Attached Files:

  2. jcsd
  3. Jan 11, 2019 #2

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes it's the displacement. If the velocity is a scalar (one-dimensional motion) it's a simple positive or negative displacement. If it's a 2D or 3D velocity vector, we integrate each coordinate separately and get an overall 3D displacement vector as the result. Adding the displacement vector to the starting point in an affine sense gives us the position at the end of the journey.
     
  4. Jan 11, 2019 #3

    opus

    User Avatar
    Gold Member

    Ok thank you, so then is it possible to find exactly the position of ##x## when we have the graph of velocity?
     
  5. Jan 11, 2019 #4

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2018 Award

    If you know the starting position and you know the displacement, then you know the current position.
     
  6. Jan 11, 2019 #5

    opus

    User Avatar
    Gold Member

    Understood! Thank you.
     
  7. Jan 15, 2019 #6
    Actually during integration we set two limits t1 and t2 so that we get the displacement between the 2 time interval. After integration we gets the equation of displacement(with respect to time) of a particle . And when we sets the limit we get the displacement during that particular time interval. To find the actual position from origin you have to put t1=0. So we get its position as well as displacement from the origin. Thank you
     
  8. Jan 15, 2019 #7

    opus

    User Avatar
    Gold Member

    Excellent thank you.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?