Find the power needed to accelerate this elevator downward

[phase0]

Homework Statement

It is not actually a homework

Relevant Equations

F.V=P
Fnet=ma

An elevator of mass M is accelerating downward with constant acceleration A. Friction force acting on the elevator is constant and given by f (The initial speed of the elevator is zero.). Find the power generated by the engine of the elevator (in terms of M, A, g, f, and time t).

For this question I write this equation Fnet.v=P and Fnet=mg-ma-f but there is time in my question and I think I couldn't use the velocity in an appropriate way.I know that work is equals to change in kinetic energy but I am not sure how can I write an equation which involves both v and t.If you have any idea,please share with me

 

[Lnewqban]

Please, see:
http://hyperphysics.phy-astr.gsu.edu/hbase/pow.html

The engine or motor, as well as the work of friction, are resisting the free fall of the elevator.

 

[haruspex]

Fnet.v=P
Fnet=mg-ma-f

"Fnet"? You are trying to find the power generated by the engine. The equations only makes sense if 'Fnet' is the force exerted by the engine, upwards positive.
All you need to add is the relationship between v and a and you have yourself a differential equation.

The benefit of working in terms of energy is usually that it avoids involving time in the first integration step, giving the relationship between velocity and displacement. But of course velocity is dx/dt, so you still get a differential equation in x and t. Having solved that you can find v(t) and hence P(t).

So you can solve it either way, in terms of energy or forces.

 

[phase0]

Please, see:
http://hyperphysics.phy-astr.gsu.edu/hbase/pow.html

The engine or motor, as well as the work of friction, are resisting the free fall of the elevator.

you are right,this was the reason why I wrote down Fnet=mg-ma-f
I thought in free body diagram mg is oppsite direction of ma and f.But it is true that writing Fnet in left hand side of my equation was silly

 

[Delta2]

Since the acceleration is constant (as it is being given by the problem statement) which is the algebraic equation that relates velocity and acceleration and time?
Use this equation and replace velocity $v$ in the formula for power $P=F_{net}\cdot v$. Then replace $F_{net}=mg-mA-f$ , do some algebraic manipulation, and you got yourself the answer.

EDIT: @haruspex is right, by $F_{net}$ here we mean the force on the elevator by the engine and not the "classical" $F_{net}$ which is always equal to $ma$.