State and prove Newton’s second law of motion.


Show that F = ma.

Difficulty: Medium

Newton’s second law of motion:

           When a net force acts on a body, it produces acceleration in the body in the direction of the net force. The magnitude of this acceleration is directly proportional to the net force acting on the body and inversely proportional to its mass.


 Derivation of formula F = ma:

          If a force produces an acceleration ‘a’ in a body of mass ‘m’, then we can state mathematically that

a \: \alpha \: F...... (1)

and    $a \: \alpha\frac{1}{m}$

By combining (i) and (ii)

Or   $a \: \alpha\frac{F}{m}$

Or   $F \: \alpha \: ma$

Putting k as proportionality constant, we get

F = kma...... (iii)


 In SI units, the value of k comes out to be 1. Thus Eq. (iii)

                            F = ma