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How do i find acceleration and x/y coordinates given time and i/j values?

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data

    At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of i = (3.00 i - 2.00 j) m/s and is at the origin. At t = 2.70 s, the particle's velocity is = (9.30 i + 6.90 j) m/s.

    (a) Find the acceleration of the particle at any time t.
    = m/s2

    (b) Find its coordinates at any time t.
    x = m
    y = m

    I tried following a similar thread but just jot confused. please help




    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 16, 2012 #2

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    Welcome to PF, piercegirl! :smile:

    Let's start with the relevant equations.
    You should have:
    $$\mathbf{\vec v}_t = \mathbf{\vec v}_0 + \mathbf{\vec a} t$$
    Do you?


    What do you get when you fill in what you have?
     
  4. Sep 16, 2012 #3
    Hello thanks for replying. Please bare with me (my professor has us doing web assign and he hasnt covered most of these topics)

    → → →
    v =v(not)+at


    v=(-9.81)2.70

    =-26.46

    This is horrible, :( Im thinking this isnt right?
     
  5. Sep 16, 2012 #4

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    Hmm, I think you haven't got your symbols straight.
    Let me list them.

    ##\mathbf{\vec v}_0## is the initial speed as a vector.
    You have it as (3.00 i - 2.00 j).
    Do you know what that "i" and "j" mean?

    ##\mathbf{\vec v}_t## is the speed at time t as a vector.
    Do you have that?

    ##\mathbf{\vec a}## is the as yet unknown constant acceleration vector, which is asked for.
    It is not the acceleration of gravity (which is 9.81 m/s).
    Leave it as it is for now.

    Can you fill in the numbers, or rather the vectors, you have in the formula?
     
  6. Sep 16, 2012 #5
    I believe i is x and J is Y. How can i get the average velocity vector by x and y?

    I trying to do delta r/delta t.

    I was given the particles velocity 9.30x+6.90 at t=2.70s
     
  7. Sep 16, 2012 #6

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    The i and j indeed represent x and y.
    They denote a vector.
    The vectors you have need to be inserted in the formula.
    I'm afraid that the formula delta r/delta t won't work for your purpose.

    Can you just replace the symbols by the respective vectors?

    So replace v0 literally by (3.00 i - 2.00 j), etcetera, without doing anything else?
     
  8. Sep 16, 2012 #7
    like this?

    (9.30i+6.90j)=(3.00i-2.00j)+ a(2.70)

    a=6.3i+8.9j/(2.70) i combined like terms...
     
  9. Sep 16, 2012 #8

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    Yep!
    That's it.

    That is your answer for part (a).

    You should include extra parentheses btw.
    Like this:
    a=(6.3i+8.9j)/2.70
     
  10. Sep 16, 2012 #9
    yay!! :) thank you so much!!! :D now for part b. how do i find the x and y components? is it just x=6.3i and y=8.9j?
     
  11. Sep 16, 2012 #10

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    No. The x and y coordinates are not constant, so that can't be right.

    You need a slightly different formula.
    $$\vec x_t = \vec x_0 + \vec v_0 t + \frac 1 2 \vec a t^2$$
    Did you have that formula?

    Now "t" is the unknown, since you're supposed to find the result "for any t".
    Can you fill in the rest?
     
  12. Sep 16, 2012 #11
    ah. I did the math and i got t=2.70. Is that right?
     
  13. Sep 16, 2012 #12

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    I haven't checked.
    But that's not what they asked.
    They asked: find its coordinates at any time t.
    So t is not just 2.70...
     
  14. Sep 16, 2012 #13
    oh! so we are solving for Vt?
     
  15. Sep 16, 2012 #14

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    No, we are solving for Xt, that is, the position at some time t.
     
  16. Sep 16, 2012 #15
    is there such a formula? It seems like the kinematic eq's keep changing :/
     
  17. Sep 16, 2012 #16

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    See my previous post #10.
    Do you have that formula?
     
  18. Sep 16, 2012 #17
    see it. My apologies, for some reason i didnt see it before. I got t=.90 but idk
     
  19. Sep 16, 2012 #18

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    Can you literally fill in the numbers/vectors you have in that formula without doing anything else?
     
  20. Sep 16, 2012 #19
    so shall i let t= to some random num and solve for xt?
     
  21. Sep 16, 2012 #20

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    Don't fill in t or xt.
    Only the others, since you should have all of them.
     
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