Now we actually come to the first bit of real physics. You see, what we've done up to now has been entirely math: vectors, and problems involving derivatives. We didn't posit any laws of nature, just what happens if say a particle has a constant acceleration. But constant acceleration isn't a general law of physics. It's an approximation to what happens when quite large heavy objects are thrown close to the surface of the earth. So now we'll see how physics really works and discover the amazing predictive power of what is known as ``Newtonian mechanics''. By the way, we shouldn't be too quick to attribute all of this to Sir Isaac. He was a brilliant man but history has a way of burying the names of many worthy people, for example Robert Hooke, who probably has a lot more to do with the invention of mechanics than most physics textbooks will admit.
So what we'll be working with are ``forces''. These have the units of mass times acceleration. Forces are vectors. That's crucial to remember. Failure to do so will likely result in wrong answers. Many forces act on a single object. One obvious example is the force of gravity. It's what keeps pushing you down so you don't accidentally fly off into outer-space. But what keeps you from being pushed down to the center of the earth? (Which has a habit of being rather unpleasant, even at this time of year.) Well if you're sitting down, then the chair is pushing up against your tushy. If you're standing up, the ground pushes up against your feet. If you have a dog, then that dog might be pulling at your pants. This also results in a force. So there are all these forces acting on a single object. Some pushing left, others right, some up, some down, some sideways. You get the idea. What's a poor object to do?
Well assuming your object is a point, then we know what to do. Unfortunately this is not very likely in my case seeing all the twinkies I've been eating. But no matter, even if you're not a point, but you're extremely rigid, like the way candies get when you leave them in the fridge too long, then we can also say what to do about all these forces. There's a special point in an object called the center of mass, and we'll discuss that a bit later. This point acts in a very simple way, so we'll just discuss the motion of that particular point and in subsequent discussion, it's really this point that's being discussed.
The upshot of all this is that to get the motion of the object ( or more correctly it's center of mass) what's important is the net force acting on the object. By net force I mean you add up all the force vectors acting on the object. That's your net force.