"If a force acts on a body the acceleration it produces is proportional to the size of the force and inversely proportional to the mass of the body."

Like Newton's 1^st law of Motion, the 2^nd law is concerned with the way moving objects behave. The 2^nd law has two parts, firstly it explains that the greater the force on an object the greater will be its change in speed or velocity or acceleration. The second part of the law states that for a given force, acceleration is inversely proportional to the mass of the object.

In Newton's own words
(To be read only for historical insight. The mixture of old English and terminology can confuse!)

The alteration of motion is ever proportional to the motive force impressed; and is made in the same direction of the right line in which that force is impressed.

If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed in the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both. "Principia - 1726"

Part 1 - more force for more acceleration
Ever tried pushing a car alone! Get some friends to help. "Many hands make light work". Four people pushing a car will move it easily, as long as they all push in the same direction. What would happen if two push on the back and two on the front? Chances are the car would not move! All are still pushing hard, but their efforts are cancelling each other out.

Today we call "altering the motion", acceleration and any change in motion, whether it be in speed or direction, is considered an acceleration. Acceleration requires force and if you wish to increase the speed of your car quickly you will require lots of force.

Acceleration is always in the same direction as the resultant force. When two or more forces are exerted the addition of these forces will change the motion of the body in the direction of the total force.

Part 2 - more mass, less acceleration
Pushing a bike is a lot easier than pushing a car, Newton's 2^nd law expresses this as "… the acceleration is inversely proportional to the mass of the body."

For the same force, the heavier an object, the less will be its acceleration. Put another way, to accelerate a massive object requires more effort that a lighter object.

F = ma
By putting the two parts together the mathematical equation F = ma is produced. This simply states that the force exerted on a body is equal to the mass of the body multiplied by its acceleration. Mass is measured in kilograms (kg), acceleration in metres per second per second (m/s/s), and force in Newtons (N). A body with a mass of 1 kg, accelerating at 1 m/s/s, is being pushed by a resultant force of 1N.