Question

How much power is needed to accelerate an object with a mass of `5 kg` and a velocity of `3 m/s` at a rate of `2 m/s^2`?

Answer 1

`30W`

Explanation:

I assume the question meant to say "to" a velocity of 3.

Consider the following 4 definitions :

Power is the rate of doing work : `P=W/t`.

Work is the inner product of the resultant force with the displacement moved in the direction of the resultant force : `W=intvecF*d vecx`.

Velocity is the rate of change in displacement : `vec v= (dvecx)/(dt)`.

Now putting all together we get :

`P=W/t=(vecF*x)/t=vecF*vecv`.

Now furthermore, from newton's 2nd Law of motion we get that `sumvecF=mveca`, where acceleration is the rate of change in velocity : `veca=(dvecv)/(dt)`.

We can hence find the resultant force in the above question as follows :
`sumF=m(dv)/dt`

`=5xx2=10N`.

Hence the power required is `P=Fv=10xx3=30W`.