Question

An object of mass 24kg is accelerated up a frictionless plane inclined at an angle of 37⁰ with the horizontal by a constant force .starting at the bottom from the rest, it covers a distance of 18m in 3 seconds
1) what is the average power required to accomplish the process ?
2)what is the instantaneous power required at the end of the 3 second interval ?

Answer 1

Find the resultant acceleration:

$$a=\frac{2d}{t^2}.$$

Find the net force:

$$F=ma=\frac{2md}{t^2}.$$

Find the average velocity:

$$v=\frac dt.$$

1) The average power is the force times average speed:

$$P=\frac{2md^2}{t^3}=576\text { W}.$$

2) Find the final speed at the end of 3rd second:

$$v_f=at=\frac{2d}{t}.$$

The instantaneous power is

$$P_i=Fv_f=\frac{4md^2}{t^3}=2P=1152\text{ W}.$$