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Solving for the length of velocity of a particle in space (Calc III, due Tomorrow!)

  1. Sep 28, 2008 #1
    1. The problem statement, all variables and given/known data
    r(t) is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then find the particle's speed and direction of motion at the given value of t. Write the particle's velocity at that time as the product of its speed and direction.

    r(t)=(2cost)i+(3sint)j+4tk; t=pi/2


    2. Relevant equations
    sin^2+cos^2=1
    length of v= sqrt(vi+vj+vk) if vi is the first coefficient of velocity equation, vj 2nd, vk 3rd.


    3. The attempt at a solution
    v(t)= (-2sint)i+(3cost)j+4k

    |v(t)| (length)=2sqrt(5), but I don't know how to get this.

    sqrt(((-2sin(t))^2)+((3cos(t))^2)+(4^2))
    sqrt((4sin^2(t))+(9cos^2(t))+(16))
    ?
    Are you supposed to somehow remove the coefficients to use cos^2+sin^2? I tried this to no avail. I also tried using the sin^2(x)= (1-cos2x)/2, and the cos one too, but that didn't work either.
     
  2. jcsd
  3. Sep 28, 2008 #2
    Re: Solving for the length of velocity of a particle in space (Calc III, due Tomorrow

    It looks to me like you have the correct answer. Just put t=Pi/2 into your last expression. You get sqrt(20) which is the same as 2sqrt(5).
     
  4. Sep 28, 2008 #3
    Re: Solving for the length of velocity of a particle in space (Calc III, due Tomorrow

    Ah, I see! Plug in before trying to simplify. That's very easy, just out of the normal order of operations I'm used to. Thanks a lot!
     
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