Deduce the equation of a force using Newton's second law of motion .

Explanation

(i) Let "m" be the mass of a moving body, moving along a straight line with an initial speed 'u'.
(ii) After a time interval of 't' second , the velocity of the body changes to 'v' due to the impact of an unbalanced external force F.
(iii) Initial momentum of the body ` to P_i="mu"`
(iv) Final momentum of the body ` to P_t=mv`
Change in momentum ` to Deltap=P_f=P_i`
=mv-mu
By Newton's second law of motion .
Force , F ` prop` rate of change of momentum
`F prop` change in momentum / time
`F prop` (mv-mu)/t
F=km(v-u)t
Here , k is the proportionality constant. k=1 in all system of units . Hence ,
`F=(m(v-u))/(t)`
Since , acceleration = change in velocity / time , `a=(v-u)//t` .
(vi) Hence , we have `F=mxx a `
Force= mass ` xx ` acceleration