Power of Crane: Changing Resultant Force & Acceleration

[adjacent]

This crane is lifting a 1Kg Box.Gravity exerts 10N on this.The crane uses 11N on lifting the box-That means the box is accelerating at 1m/s².This also means it travels more and more distance in one sec as it rise(because of acceleration).This means that the work done by lifting the box also increase as the box rise ,in a second(As the resultant force is 1N and the rate of distance increasing increases with time)It follows that the power of the crane in changing.
But when calculating power ,we generally do not account for this.Why?

 

[PhanthomJay]

Sometimes the word 'power' and 'average' power are used to describe the same thing, but in actuality, there are 2 definitions for power, average power and instantaneous power. When the speed is constant, they are the same. When acceleration is involved, they are not.