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At a certain instant, a particle-like object is acted on by a force F = (4.0 N) ihat - (3.0 N) jhat + (9.0 N) khat while the object's velocity is v = - (2.0 m/s) ihat + (4.0 m/s) khat. What is the instantaneous rate at which the force does work on the object?

(b) At some other time, the velocity consists of only a j component. If the force is unchanged, and the instantaneous power is -12 W, what is the velocity of the object just then?
m/s jhat

  • physics -

    Both questions can be answered using the fact that the rate of doing work (the instantaneous work) is the dot product of V and F vectors.

    (a) W = F*V = (4)(-2) + (-3)(0) + (9)(4) = 36 - 8 = 28 W

    (b) Let the object's velocity be V*jhat
    -12 = F*V = -12
    = (-3)(V) = -12
    V = 4 m/s, in the j direction

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