Source: High school physics (Chinese)
Problem Sets:
Problem
As shown in Figure below, an object is lifted by an ideal movable pulley. A constant pulling force $F$ is applied, causing the object to accelerate upwards from rest at a constant acceleration $a_{obj}$.
P0485-problem-1
For a movable pulley, the point where the force $F$ is applied moves at twice the speed of the object. Let $v_F$ be the velocity of the point of application of the force and $v_{obj}$ be the velocity of the object. Then $v_F = 2v_{obj}$. Similarly, the accelerations are related by $a_F = 2a_{obj}$.
The velocity of the point where the force is applied at time $t$, starting from rest, is:
$$v_F = a_F t = (2a_{obj})t$$The instantaneous power $P$ delivered by the force $F$ is:
$$P = F v_F$$Substituting the expression for $v_F$:
$$P = F(2a_{obj}t)$$