Calculating the power for acceleration of an elevator An elevator does need some kind of acceleration when it starts to rise up so there has to be s force acting on it. But it surely does not accelerate the whole time so after some distance or time it reaches a speed and stops to accelerate. In an old physics textbook I found an example where the power a motor would need to lift it was calculated like this
P = F * v
But they did not take the average speed for v but the speed which would be reached at the end of the acceleration. Why was this speed used and not the average speed? 
 A: What are you trying to calculate? The average power OR the instantaneous Power at the end of the acceleration? 
The first part will be calculated by taking the average force/acceleration along with the average speed.
The second part will be calculated using the final speed after acceleration and multiplying it by the weight of the lift + passengers (as this is the amount of force required to maintain a constant speed).
Please post the exact question you want answered.
Edit:
Do not make two posts regarding the same question.
A: 
But they did not take the average speed for v but the speed which
  would be reached at the end of the acceleration.

It might be because the acceleration ends quickly so that the speed is constant for a much longer period of time than the acceleration lasts.
I was unable to find any data on the duration of acceleration of an elevator, so I don't have any data to support this. But it seems to me the times I have used an elevator the initial sensation of it pushing up on me generally seems to be brief. In other words, it is possible that for most elevators the duration of the upward acceleration is probably a lot shorter than the duration of constant velocity, so that most of the power needed is to keep the elevator going at constant velocity. That could be the reason for using $P=Fv$. 
I would think that during the initial acceleration what is more critical is the torque that the motor can deliver to get it started. 
Hope this helps.
