(a) At a certain instant, a particle-like object is acted on by a force F= (5.7 N)i -(2.7 N)j + (5.0 N)k while the object's velocity is v= -(2.3 m/s)i + (5.8 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 y component. If the force is unchanged, and the instantaneous power is -8.70 W, what is the velocity of the object just then? (Give your answer without a unit vector.)

(a) The force which works on the object at a rate 15.89 w.

(b) The velocity of the object when the power is -8.7 w is .

Explanation:

Work: The  work on an object is the dot product of force that acts on the object and velocity of the object .

P = F.V

Dot product:

where the angle between a and bis θ  

(a)

Given that,

and

The work on the object is

=

={(5.7)×(-2.3)+(-2.7)×0+(5.0×5.8)} w

=15.89 w

The instantaneous rate at which the force does work on the object is 15.89 w.

(b)

The velocity of the object consists of only a y component i.e the x component and y component are zero.

and

Let,

The power is -8.70 w.

∴ -8.70 =

⇒ - 8.70 = -2.7×a

⇒ a = 3.22

The velocity of the object is

what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.