(a)At a certain instant, a particle-like object is acted on by a force F = (4.0 N)i - (2.0 N)j + (9.0 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?

Question

(a)At a certain instant, a particle-like object is acted on by a force F = (4.0 N)i  - (2.0 N)j  + (9.0 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?

bobpursley · Answer

work=force dot dx the dot product is scalar, so all the components (ii,jj,kk) are added. b) power= d work/dt= d Force dot velocity/dt -12watts= (4i-2j+9k) vj vj= -12/-2 = 6j