WEll, in reply to the original question, i may give some reasons why f=ma and not mv :
First, a body having no net external force which acts on travels with const. velocity where the constant can be zero. So we need something called 'Force' to explain changes in motion, not the motion itself. It's acceleration that is the measure of changes in motion. We define force such that it is proportional to the acceleration. The constant differs from object to object, and we denote it by 'm' and call it 'mass. So, we write f=ma .