This law defines the relationship between force, mass and acceleration. It seems reasonable to accept that

(i)                  for a body of a particular mass, the bigger the force is, the bigger the acceleration will be

(ii)                the larger the mass is, the larger will be the force needed to produce a particular acceleration.

Experimental evidence verifies that the force F is proportional both to the acceleration a and to the mass m.

i.e. F µ ma

or  F = kma where k is a constant

Now if m = 1 and a = 1 then F = k,  so the amount of force needed to give a mass of 1 kg an acceleration of 1m/s^2 is given by k.

If this amount of force is chosen as the unit of force we have k = 1 and

F = ma

The unit of force is called the Newton (N) and is defined as the amount of force that gives an acceleration of 1 m/s^2.

It is important to take note that acceleration and force are both vector quantities and that mass is scalar. And if p = kq , then p and q  are parallel vectors.

Therefore, from the equation F = ma we see that:

The vectors F and a are parallel, i.e. the direction of an acceleration is the same as the direction of the force that produce it.

When more than one force acts on a body, F represents the resultant force.

If the force is constant the  acceleration also is constant and, conversely, if the force varies, so does the acceleration.

If the acceleration is zero, the resultant force is zero – in other words Newton’s first law follows from the second.

To sum up:

The resultant force acting on a body of constant mass is equal to

The mass of the body multiplied by its acceleration.

F ( N ) = m ( kg ) x a ( m/s^2 )

The resultant force and the acceleration are in the same direction.