a) At a certain instant, a particle-like object is acted on by a force F = (3.0

Question

a) At a certain instant, a particle-like object is acted on by a force F = (3.0 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?

I converted the vectors into magnitudes now I'm just stuck.... any help?

Explanation / Answer

(a) F = 3i - 3j + 9k v = -2i + 4k Rate of work done = F . v                               = (3i - 3j + 9k) . ( -2i + 4k)                               = -6 + 36                               = 30 watt (b) F = 3i - 3j + 9k Let v = x j P = -12 watt -12 = F . v F = 3i - 3j + 9k Let v = x j P = -12 watt -12 = F . v -12 = (3i - 3j + 9k) . (x j) -12 = -3x    x = 4 v = 4 j

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