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Vectors, velocity in terms of unit vectors

  1. Nov 1, 2011 #1
    1. The problem statement, all variables and given/known data

    A particle moving in xy plane has velocity components in x and y directions
    Dx/dt = b1+c1t and dy/dt = b2+c2t

    A) integrate above equations to give displacement components x and y as functions of time
    B) write the velocity (v) of the particle at time t in terms of initial vectors I and j
    C) find acceleration a of the particle in terms of unit vectors I and j
    D) write an expression for magnitude of acceleration
    E) find an expression for the time at which v and a are perpendicular

    I have integrated the equations to give x=b1t+(c1t^2)/2+ constant (x0)
    And y=b2t+(c2t^2)/2+ constant (y0)

    Do not know what to do next :/
    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 1, 2011 #2

    I like Serena

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    Homework Helper

    Welcome to PF, Vandella! :smile:

    The velocity is the vector (dx/dt, dy/dt), or written with i and j:
    v=(dx/dt)i + (dy/dt)j.

    To find the acceleration vector, you need to take the derivative.
     
  4. Nov 1, 2011 #3
    Thanks for the welcome :) and for the reply

    I had written exactly what you had posted but had talked myself out of thinking it was correct and must be much more difficult
     
  5. Nov 1, 2011 #4

    I like Serena

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    I have to admit at being surprised that you could integrate the expressions and then not set up the vector for the velocity. :wink:

    And as Occam's razor states: "The simplest explanation that fits all the facts is usually the right one!" :smile:
     
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