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 ,∆p = P f - P i = 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