Physics-calc

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Suppose the position of an object is given by ->r(vector) = (3.0t^2*ihat - 6.0t^3*jhat)m. Where t in seconds.

Determine its velocity ->v as a function of time t.

Determine its acceleration ->a as a function of time t.


Determine ->r at time t = 2.5 s.

Determine ->v at time t = 2.5s.

Express your answer using two significant figures. Express your answer in terms of the unit vectors ihat and jhat.

  • Physics-calc -

    This is a problem of differentiation where the independent variable is t, and
    r is the position vector.
    v is the velocity vector.
    a is the acceleration vector.

    The motion is described in two orthogonal directions i and j, which means that you can do the calculations in each of the directions independently of each other.

    Given
    r = (3.0t^2i - 6.0t^3j) m
    The i and j components of the position vector are
    Pi(t)=3.0t^2
    Pj(t)=6.0t^3

    So d(Pi(t))/dt = d(3t²)/dt = 6t
    ...
    can you complete the rest?
    Post your answers for a check if you wish to.

  • Physics-calc -

    What it P representing? Position?

  • Physics-calc -

    6t-18t

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