Is v the speed of the object or the speed of the rope in the pulley?

Is v the speed of the object or the speed of the rope in the pulley?

Power is the ratio of work to the time needed to do the work. The physical meaning is the amount of work done per unit time, which describes the speed of work. By definition, P = w / T, w = FS, v = s / T, so p = FV. Then f in the formula is the external force on the body, V is the velocity, which means that power equals the product of the force on the body and the velocity