Physics/Math

At a certain instant, a particle-like object is acted on by a force F = (3.0 N) i - (1.0 N) j + (8.0 N) k while the object's velocity is v = - (2.0 m/s) i + (4.0 m/s) k. 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?

a) the Dot product of force and velocity is power.

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