physics

A particle has ⃗r(0) = (4 m)j and ⃗v(0) = (2 m/s)i.
If its acceleration is constant and given by ⃗a = −(2 m/s2) (i +j), at what time t does the particle first cross the x axis?
Answer in units of s.

part 2. At what time t is the particle moving parallel to the y axis; that is, in the j direction?
Answer in units of s.

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  1. Let u = x direction velocity (i) and v = y direction (j) velocity

    Xo = 0
    Yo = 4

    Uo = +2
    Vo = 0

    Ax = -2
    Ay = -2

    u = Uo + Ax t
    u = 2 - 2 t

    x = Xo + Uo t +(1/2) Ax t^2
    x = 2 t - t^2

    y = Yo + Vo t + (1/2) Ay t^2
    y = 4 - t^2

    so
    y = 0 when t = 2

    u = 0 when t = 1

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  2. Thank you very much.. i understand it...it crosses the x-axis when the y point is =o, and is parallel to the y- axis when the vector in the x direction aka the slope is = to 0 =]

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