Newton,s Laws $ Derivations

Newton First Law:
                           

In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force. Mathematically: Sum of all forces = 0           or dv/dt = 0 Newton Second Law:

                                 

In an inertial reference frame, the vector sum of the force F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma. Mathematically F is directly proportional to acc 'a'.               & F is directly proportional to acc 'm'. than remove proportional sign, put = & constant 'k'.   since k=1 so, F=ma  Newton Third Law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body. Mathematically: Fa = -Fb Because Fa is action force & -Fb is reaction force.