Question

at a certain instant, a particle-like object is acted o a force f - (4.0 n)i - (2.0 x)i (9.0 n)k while the object's velocity is i - -(z.tmls)i (4.0m/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 - izw,what is the velocity of the obj ect?

Answer 1

The instantaneous power at which the force does work on the object is -4.0 watts. If the force remains unchanged and the instantaneous power is -izw, then the velocity of the object must be in the negative y direction, with zero x and z components and a velocity magnitude of 4.0 m/s.

Step-by-step explanation:

First, we need to calculate the dot product of the force and velocity vectors to find the instantaneous power. The dot product is given by:

P = F · v

= (4.0 N)(-1.0 m/s)

= -4.0 W

The negative sign indicates that the force is doing work in the opposite direction of the displacement, which means the force is slowing down the object.

(b) If the force remains unchanged and the instantaneous power is given by P = -izw, then the velocity of the object must be in the negative y direction. Since we know the x and z components of the velocity are zero, we have:

v = 0î - zĵ - 4.0k m/s