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!

Homework Help: Velocity Vector Versus Tangent Line

  1. Mar 5, 2008 #1
    I have encountered a problem in my Calculus homework.

    I have a position function, r(t)= (t^2)i + (4t)j and in my homework, I am asked to find the tangent to this curve at the point t=3. I did this by finding dy/dx, or 2t/4 @ t=3 is 6/4. However, I am also asked to relate this to the velocity vector for the position function @ t=3, but I don't understand the relationship. Would they share the same slope? Any help is very much appreciated! :-)
  2. jcsd
  3. Mar 5, 2008 #2
    Well you have the position's function. The tangent line necessarily has a slope of dr/dt, which is equivalent to the velocity so yes.
  4. Mar 5, 2008 #3
    Oh that makes sense! Thank you very much :-) But they're not the same line...are they?
  5. Mar 5, 2008 #4
    The velocity has no inherent sense of position, so you can't really compare velocity and a tangent line even at the same time t. A tangent line more or less answers the question "where would you be at some time you knew you were at position r(t) at time t and maintained a constant velocity for all time?", but don't read too far into this.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook