Results 1 to 5 of 5

Math Help - Some kinematics/vector calculus

  1. #1
    Senior Member
    Joined
    Jul 2006
    Posts
    364

    Some kinematics/vector calculus

    Hi, im having problems solving some questions:

    1. The position of a particle is given by r(t) = (2sin(3t))i + (cos(3t))j
    What is its maximum speed?

    PS: what's with the latex system? When will it be back? Should i use standard ASCII for now?

    I will post more questions in this thread if need be.

    EDIT: sorry, i realized i should post questions in separate threads, so i'll do that instead from now on.
    Last edited by scorpion007; September 13th 2006 at 12:35 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,907
    Thanks
    329
    Awards
    1
    Quote Originally Posted by scorpion007 View Post
    Hi, im having problems solving some questions:

    1. The position of a particle is given by r(t) = (2sin(3t))i + (cos(3t))j
    What is its maximum speed?

    PS: what's with the latex system? When will it be back? Should i use standard ASCII for now?

    I will post more questions in this thread if need be.

    EDIT: sorry, i realized i should post questions in separate threads, so i'll do that instead from now on.
    To find the max speed you need to find the time derivative:
    v(t) = 6 cos(3t) i - 3 sin(3t) j (This is the velocity, incidentally. You gave the displacement function, a vector.)

    What is the speed of this particle?
    v(t) = sqrt( v_x ^2 + v_y ^2) = sqrt(36 cos^2(3t) + 9 sin^2(3t))
    v(t) = sqrt(27 cos^2(3t) + 9)

    So maximum speed will occur when a(t) is 0:
    a(t) = (-162 sin(3t) cos(3t)) / (2 [sqrt(36 cos^2(3t) + 9 sin^2(3t))]) = 0

    Or when -162 sin(3t) cos(3t) = 0.

    This equation has a quite simple solution: t = 0 can be seen by inspection. I leave it to you to show that this is a maximum speed, not a minimum.

    v(0) = sqrt(27 + 9) = sqrt(36) = 6 (in whatever units you are using.)

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jul 2006
    Posts
    364
    where did you get this line from?

    So maximum speed will occur when a(t) is 0:
    a(t) = (-162 sin(3t) cos(3t)) / (2 [sqrt(36 cos^2(3t) + 9 sin^2(3t))]) = 0
    the derivative of v(t) does not yield that does it?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by scorpion007 View Post
    where did you get this line from?



    the derivative of v(t) does not yield that does it?
    Try:

    v^2=27 cos^2(3t)+9,

    then

    2v.a=-162 cos(3t)sin(3t)

    a(t)=-162 cos(3t)sin(3t)/v(t),

    which when you substitute the expression topsquark gave for v(t)
    will give the expression for a(t).

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,907
    Thanks
    329
    Awards
    1
    Quote Originally Posted by scorpion007 View Post
    where did you get this line from?



    the derivative of v(t) does not yield that does it?
    Sorry. I had made a mistake when I was writing the post out. I guess I didn't correct all of the mistakes before I posted.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Kinematics Using Integral Calculus
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: January 14th 2011, 09:52 AM
  2. Vector kinematics projectiles thrown at an angle
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: September 30th 2009, 01:58 AM
  3. Calculus - kinematics
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 3rd 2009, 05:42 PM
  4. Kinematics (Calculus Form)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 30th 2008, 07:43 PM
  5. kinematics/calculus
    Posted in the Advanced Applied Math Forum
    Replies: 6
    Last Post: October 15th 2006, 11:01 PM

Search Tags


/mathhelpforum @mathhelpforum