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#?

1 Answer
Jan 5, 2016

#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#.