Newton’s Second Law of Motion For Class 9

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:

Initial momentum , P_i = mu
Final momentum , P_f = mv
Change in momentum ,&#x2206p = P_f – P_i
       = 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