posted by franck .
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?
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