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