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Motion in Space: Velocity and Acceleration

  1. Sep 22, 2014 #1
    1. The problem statement, all variables and given/known data
    For V(t) = (1+t)i + (t^2-2t)j find:

    1. velocity
    2.Acceleration
    3. speed/length
    4. Unit Tangent
    5. tangential component
    6. normal component at t=2



    2. Relevant equations



    3. The attempt at a solution

    1. v'(t) = <1,2t-2> = <1, 2(t-1)>
    2. a(t) = <0,2>
    3. length = Square root of (1+4(t-1)^2)
    4. Unit Tangent = <1,2(t-1)> / square root (1+4(t-1)^2)
    from here i'm stuck trying to find the tangential component and normal component.
     
  2. jcsd
  3. Sep 22, 2014 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    First decide: normal and tangential component of WHAT? In general, if you have two vectors ##\vec{a}, \vec{b}## the component ##\vec{a}_{||}## of ##\vec{a}## parallel to ##\vec{b}## and the component ##\vec{a}_{\perp}## perpendicular to ##\vec{b}## are
    [tex] \vec{a}_{||} = \frac{\vec{a} \cdot \vec{b}}{\vec{b} \cdot \vec{b}} \vec{b} \\
    \vec{a}_{\perp} = \vec{a} - \frac{\vec{a} \cdot \vec{b}}{\vec{b} \cdot \vec{b}} \vec{b}[/tex]
     
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