A method and apparatus for use in controlling a dispensing rate of medication or other substance via a syringe, including, without limitation, into a patient, intravenous line port or heparin lock. A force (typically manual) is applied to an input plunger of a dashpot, which is directly coupled to a piston which, in turn, is coupled to an output plunger. The force applied to the input plunger is buffered and transmitted to the output plunger. The output plunger acts upon the plunger of a conventional syringe, thereby resulting in flow of medicine or any other substance from the syringe at a desired and controlled flow rate.