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 Force   Change in momentum / Time taken

Consider a body of mass m having an initial velocity u.The initial momentum of this body will be mu.Suppose a force F acts on this body for time t and causes the final velocity to become v.The final momentum of this body will be mv.Now,the change in momentum of this body is mv - mu and the time taken for change is t.So,according to Newton's second law of motion :

                          F   mv - mu / t

or                        F   m(v - u)/t

But (v - u)/t represents change in velocity with time which is known as acceleration 'a'.So,by writing 'a' in place of v - u / t in the above relation,we get :

                                      F   m x a 

Thus,the force acting  on a body is directly proportional to the product of 'mass' of the body and 'acceleration' produced in the body by thye action of the force , and it acts in the direction of acceleration .This is another definition of Newton's second law of motion.

The relation    F   m x a can be turned into an equation by putting in a constant k.

Thus,                F = k x m x a           (where k is a constant )

The value of constant  k in SI units is 1,so the above equation becomes :

                          F  = m x a 

or                 Force = mass x acceleration

Thus Newton's second law of motion gives us a relationship between 'force' and 'acceleration'.