The basis for Newtons theory of mechanics are the following three laws. The velocity of a body on which no net forces act cannot change In everyday life friction is almost universally present so that to achieve motion we need to apply a force which compensates for friction ie. For 2000 years this experience perpetuated the view of Aristoteles that a driving force is necessary to induce motion. Perhaps if civilization had developed further from the equator where lakes freeze in the winter this notion would have been challenged sooner. Newton provided the mathematical framework for this observation.
Acceleration requires a force.
From the equation we see that the unit for force is Newtons second law is the first time the mass of a body enters our description of physics. From the pendulum to the dime and feather mass did not enter our formulae. Newtons second law introduces mass as a scaler which determines how much force is required to accelerate, to change the velocity of, a body. The greater the mass the smaller the acceleration for a given force. As you have already seen in homework problems due this week Newtons second law is a vector relation.