# Newton's Second Law

## Resulting force produces acceleration

If a body is at rest (relative to a certain frame), its velocity is zero. If it is set in motion, its speed will no longer be zero and therefore the object has been accelerated. Similarly, if a body in straight and uniform motion (and thus with zero acceleration, since the velocity is constant) is forced to stop, we can also say that it has accelerated (popularly in this case "slowdown").

Newton's First Law, in both situations - from rest to rectilinear and uniform motion or otherwise - a resultant force acts on the body.

From this we conclude that the actuation of a resultant force upon a body produces in it an acceleration.

This is the theme of Newton's Second Law, which we will see below.

Understanding, through experiments, the relationship between force and acceleration is not an easy task due to the complications of friction and air resistance.

Imagine a 1 kg block of dough resting on a perfectly smooth surface. Subjected to the action of a resulting horizontal force of intensity F, this block acquires an acceleration of 1 m / s2, as illustrated in A. If the same resulting force acts on the mass block 0.5 kg, the acceleration acquired will be 2 m / s2, according to B.

If a resulting horizontal force twice the intensity of 2F acts on a 1kg block of mass, it acquires acceleration of 2m / s.2 (see C), and if it acts on a block of mass 0.5 kg, it acquires acceleration of 4 m / s2 (see D). Do you realize the mathematical regularity involved?

Looking at the example above

Comparing THE and ÇWe realize that when the resulting force acting on a certain body is doubled, the resulting acceleration also doubles. The same conclusion can be drawn by comparing B and D. Many such experiments allow for the following generalization.

In words: The acceleration of a body is directly proportional to the resulting force acting on it.

Comparing B and Ç, We find that if the mass of one body is twice that of another, the resulting force must be doubled to accelerate it equally. Several experiments like this lead to the following conclusion.

In words: The resulting force that produces some acceleration in a body is directly proportional to its mass.

Finally, comparing THE and BWe find that if two bodies are subjected to the same resultant force and if one has half the mass of the other, then it will acquire twice the acceleration. The same conclusion can be drawn by comparing Ç and D. This can be generalized as follows.

In words: Under the action of a resulting force, the acceleration of a body is inversely proportional to its mass.

Now consider the equation and its symbology:

Fr - resultant force modulus acting on a body

m - body mass

a - body acceleration

We can mathematically state the conclusions drawn above.

 In equation: 