physics
posted by franck .
At a certain instant, a particlelike 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?
W
(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

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