Theory:

Consider an object of mass, \(m\) with an initial velocity, \(u\) is moving along a straight line. It is in uniform acceleration with velocity, \(v\) in time, \(t\) by a constant force, \(F\).
 
Initial momentum of the object, \(p_1\) \(=\) \(m\ u\)
Final momentum of the object, \(p_2\) \(=\) \(m\ v\)
 
Changeinmomentumαp2p1αmvmuαm×vuRateofchangeofmomentumαm×vut
 
Fαm×vutF=km×vut
 
Where \(k\) is the constant of proportionality.
 
F=kma
 
Here, a=vut
 
The above equation, which implies the rate of change of velocity, is known as acceleration.
Unit of force:
We know that the SI units of mass is \(kg\) and acceleration is \(m\ s^{ –2}\). The unit of force is selected in such a way that the value of the proportionality constant, \(k\) is one.
A unit of force is known as the amount of force that causes an acceleration of \(1\ m\ s^{ –2}\) in an object having \(1\ kg\) mass.
1unitofforce = k×1kg×1ms2
 
Hence, the value of \(k\) becomes one and makes F=ma.
 
The SI unit of force is \(kg\ m\ s^{ –2}\) or newton (\(N\)). The value of one newton is written as,
\(1\ N\) \(=\) \(1\ kg\ m\ s^{ –2}\)
The second law of motion implies that the force (\(F\)) acting on an object is a product of its mass (\(m\)) and acceleration (\(a\)).
 
F=ma