Newton’s Second law of motion: It states that rate of change of momentum is directly proportional to unbalance external force. And change of momentum is in the direction of unbalance force.
Mathematical Derivation:

Mathematical Derivation of Newton

Initial momentum , Pi = mu
Final momentum , Pf = mv
Change in momentum ,&#x2206p = Pf – Pi
       = mv – mu
But we know that rate of change of momentum is directly proportional to the applied unbalanced force.
∴ F &#x221D &#x2206p/t
or F &#x221D (mv – mu ) / t/
Or F &#x221D m. ( v -u )/t
Or F &#x221D m. a , Where a= Acceleration
Or F = k. m. a ,
Or F = 1. m. a , In SI system K=1
F = m. a

READ :  Newton's First Law of Motion Class 9 | Law of Inertia

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