Particle trajectories

  1. 1. The problem statement, all variables and given/known data

    At time t = 0, a particle is located at the point (1, 2, 3). It travels
    in a straight line to the point (4, 1,4), has speed 2 at (1, 2, 3) and
    constant acceleration 3i - j + k. Find an equation for the position
    vector r(t) of the particle at time t.

    2. Relevant equations



    3. The attempt at a solution
    If we integrate the acceleration vector twice, we get the position vector (along with some constants we must determine). Plugging in the initial position vector gives us

    [tex] r(t) = <1.5t^{2},-.5t^{2},.5t^{2}> + v_{0}t + <1,2,3>[/tex]

    The problem is I don't know how to find the initial velocity. That's all I need to complete the problem. I know the speed at time t=0, but not the velocity. I also know that the particle travels in a straight line, meaning its unit tangent vector is constant and that its motion is nonperiodic, but how does that help?

    BiP
     
  2. jcsd
  3. Ray Vickson

    Ray Vickson 6,305
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    If a particle travels in a straight line, how are the velocity and acceleration vectors related?

    RGV
     
  4. LCKurtz

    LCKurtz 8,391
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    That equation doesn't make any sense because you can't add vectors and scalars. And remember you can always express a velocity vector as the speed times a unit vector in the correct direction.
     
  5. Where in my equation did I add vectors with scalars? Every term in my equation is a position vector...

    BiP
     
  6. haruspex

    haruspex 14,333
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    If it travels in a straight line then its acceleration must always be collinear with the velocity.
     
  7. LCKurtz

    LCKurtz 8,391
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    Well, you mentioned that the initial speed was 2. Since there was no definition given for ##v_0## and it looks like a scalar, I assumed it was ##2##. And there is no notation to distinguish vectors from scalars, I assumed ##v_0 t## was a scalar.
     
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