If you push harder, you get more acceleration, but how much more?
The relationship between force and acceleration turns out to be quite simple: If you push twice as hard, you get twice the acceleration. If you push three times as hard, you get three times the acceleration. Four times the force produces four times the acceleration, etc.
This type of a relationship (double one thing, the other doubles) is called a direct proportion or direct variation. In other words,
The net force also determines the direction of the acceleration -
A force applied to an automobile will not have the same effect as the same force applied to a pencil. An automobile resists accelerating much more than a pencil does, because it has more inertia, or mass.
The acceleration of an object depends not only on how hard you push on it, but also on how much the object resists being pushed.
What is the effect of mass on acceleration? This, too, turns out to be quite simple (I wonder why...). For the same force, an object with twice the mass will have half the acceleration. If it had three times the mass, the same force will produce one-third the acceleration. Four times the mass gives one-fourth of the acceleration, and so on.
This type of relationship between quantities (double one, get half the other) is called an inverse proportion or inverse variation. In other words, then:
"If the net force on an object is not zero, the object will accelerate. The direction of the acceleration is the same as the direction of the net force. The magnitude of the acceleration is directly proportional to the net force applied, and inversely proportional to the mass of the object."
Mathematical symbols provide a convenient shorthand for all of this: