Imagine a massless and frictionless pulley with two weights hanging either side of the pulley by a massless string.
Rather than being fixed to a ceiling, the pulley is being pulled upward by an external force F, with the weights and string still attached.
Due to Newton's 2nd Law,
where $T$ is the tension in the string on either side of the pulley and $a$ is the vertical acceleration of the pulley.
Clearly, since there is a net upward force, the pulley itself will accelerate upwards.
But because the $m=0$,
Does this not then suggest that the pulley has a constant velocity?