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Acceleration. Component Form.

  1. Jun 18, 2008 #1
    1. The problem statement, all variables and given/known data
    A particle moves in the xy-plane with constant acceleration. The particle is located at r= (2i + 4j)m at t=0 s. At t=3 s it is at r=(8i - 2j) m and has a velocity v= ( 5i - 5j) m/s.
    a) What is the particle's acceleration vector a?
    b) What are its position, velocity and speed at t= 5s?

    2. Relevant equations
    xf= xo + vt+ 0.5 a t^2
    yf= yo + vt+ 0.5 a t^2

    3. The attempt at a solution

    I used the above two equations to solve for the acceleration in both x and y components separately and I got a= (1.33i - 1.33j), but the answer at the back of the textbook is a= (2i - 2j). I don't understand what I'm doing wrong. Can someone guide me please? Thanks in advance!
  2. jcsd
  3. Jun 18, 2008 #2
    Show us the steps you took to get the 'wrong' answer.
  4. Jun 18, 2008 #3


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    Homework Helper

    Hi habibclan,

    In your equations, the v is the initial velocity, and it appears that you plugged in 0 for that. However, this particle does not start at rest, and the initial velocity is unknown. (So your x equation, for example, has two unknowns--the initial velocity in the x direction and the acceleration in the x direction.)

    However, you do also know the final velocity in the x direction. Do you see what to do with that?
  5. Jun 18, 2008 #4
    For the equation, i plug in the initial and final x-component position, the initial velocity as 0, and t=3 s and solve for a.

    xf= xo + vt+ 0.5 a t^2
    8 = 2 + 0.5*a * (3^2)
    a= 1.33

    Therefore, the acceleration of the x-component is 1.33 m/s^2

    For this one, its the same as above, except i plug in the intial and final y-comp. positions.

    yf= yo + vt+ 0.5 a t^2
    -2=4 + 0.5*a* (3^2)
    a= -1.33

    Therefore, acceleration of the y-comp. is -1.33 m/s^2.

    What am I doing wrong please?
  6. Jun 18, 2008 #5
    The initial velocity is unknown you'll have to solve 2 equations with two unknowns.
  7. Jun 18, 2008 #6
    I got it!!! Thank you so much! I used the equation vf= vi + at to solve for initial velocity and then plugged it in. Stupid of me to assume that the initial velocity was 0. Thanks a lot!
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