Force and momentum:

         Consider a body of mass m moving with initial velocity vi, let a force acts on the body which produces an acceleration an in it. This changes the velocity of the body. Let its final velocity after time t become vf. If pi and pf be the initial momentum and final momentum of the body related to initial and final velocities respectively then

                      Pi=mvi

                      Pf=mvf

Or 

           Change in momentum = final momentum – initial momentum

Or

                 P=mv

 

           Thus the rate of change in momentum is given by:

$\frac{pf \:, \: pi}{t} =\frac{mvf \: - mvi}{t}$

 

              Since $\frac{vf \:- \: vi}{t}$ is the rate of change of velocity equal to the acceleration a produced by the force F

$\frac{pf \:, \: pi}{t}$ = ma

 

According to Newton’s second law of motion,

           F= ma

 

Or $\frac{pf \:, \: pi}{t}$ = F …………… (I)

 

Equation (I) also defines force and states Newton’s second law of motion as:

When a force acts on a body, it produces an acceleration in the body and will be equal to the rate of change of momentum of the body.