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A motorized pulley lifts an object of mass $m$ from rest with a constant acceleration $a = g$.

The average power delivered in time $t$ assuming that there are no frictional forces is

A

$\cfrac{mg^2t}{2}$

B

$mg^2t$

C

$2mg^2t$

D

$4mg^2t$

E

$\cfrac{mg^2t}{4}$

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