Results 1 to 3 of 3

Math Help - If x(t)=(t, sin 4t, cost 4t), 0<= t<= Pi, then how do you find the following?

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    20

    If x(t)=(t, sin 4t, cost 4t), 0<= t<= Pi, then how do you find the following?

    a) the velocity, speed, acceleration at any time t
    b) the length of arc of the curve
    c) a parameterization of the curve by arc length
    d) T, N, and K at t=pi/2
    e) the tangential and normal components of acceleration
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by keysar7 View Post
    a) the velocity, speed, acceleration at any time t
    b) the length of arc of the curve
    c) a parameterization of the curve by arc length
    d) T, N, and K at t=pi/2
    e) the tangential and normal components of acceleration
    What have you tried?

    For the first one, just like in 1d calculus the velocity is the first derivative with respect to time and the acceleration is the 2nd derivative. Speed is the magnitude of velocity
    \text{speed }=||\vec{v}||

    The arc length formula is
    s=\int_{0}^{t}||\vec{v}||dt

    for c solve part b) for t and substitute into the original equation.

    This should get you started.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    From
    Palo Alto!
    Posts
    13

    There you go... But double check!

    This question is relevant to the stuff I'm trying to learn too. So I took a stab at it.
    But could somebody check my answers below? Hope this helps Keysar too.

    Part a)
    v(t) = (1, 4 cos 4t, -4 sin 4t)
    v(t)| = √(1 + 16 cos^2 4t + 16 sin^2 4t) = √(1 + 16) = √17
    a(t) = (0, -16 sin 4t, -16 cos 4t)

    Part b)
    Length of arc = √(17) pi

    Part c)
    x(t) = (s/√17, sin (4s)/√17, cos (4s)/√17)


    Part d)

    T(pi/2) =1/√17 (1,4,0)
    N(pi/2) =(0,0,-1)
    k=16/17

    Part e)
    Tangential component of acceleration (everywhere) = 0
    Normal component of acceleration (at pi/2) = (0,0,-16)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the Cost
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: September 7th 2010, 06:38 AM
  2. Find Combined Cost
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 21st 2009, 08:15 AM
  3. Find Hourly Cost
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 13th 2008, 03:48 AM
  4. Find the Cost
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 11th 2008, 01:58 PM
  5. find cost price
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: May 25th 2008, 09:23 AM

Search Tags


/mathhelpforum @mathhelpforum