Is F=ma Newton's 2nd Laws of Motion?

That is a good question. F=ma is a special case of Newton's 2nd Law of Motion . Newton's second law states that: The rate of change of linear momentum is proportional to the applied force and acts in the same direction as the force. Newton's 2nd Law implies F=ma only if the mass of the change of momentum stays constant. Here I will write how you can get F=ma from the second law if the mass stays the same.

Final momentum: P_f=m_f x v_f , m_f is final mass, v_f is final velocity

Initial momentum: P_i=m_i x v_i , m_i is the initial mass, v_i is the initial velocity

now F is proportional to the rate of change of momentum.

F=k x (P_f - P_i)/t

F= k x ( m_f x v_f - m_i x v_i)/t

We know the mass stays the same so m_f=m_i

F= k x ( m_i x v_f - m_i x v_i)/t

Factorise m_i out

F= k x m_i x(v_f - v_i)/t

write m_i =m to make it look nicer

F= k x m x(v_f - v_i)/t

we know v_f = v_i + at from our SUVAT equations so

a = (v_f - v_i)/t by rearranging the equations

Plug this in the equation then we get

F=ma