That is something you cannot see from the first or second law and similarly, there is no way to use this to derive the second law (you cannot derive the first law because that is assumed to be valid in order to postulate the third law). It deals with interactions and states that two bodies exert same but opposite forces o each other. The third law adds something more to the first and second laws. That's what second law is for, to say that there is a linear relationship. You also cannot derive the second law from the first one because all you know from the first law is that when an object accelerates, there is a force acting but the first law says nothing about the relation between the force and the acceleration. If an observer is in a non-inertial reference frame, she will observe that the second and third laws are not valid (when you sit in an accelerating car, the Earth accelerates in the opposite direction without any force acting on it). Although it might seem you can derive it from the second law (if the net force is zero, there is no acceleration and the velocity is constant) but in fact, both second and third law assume that the first law is valid. The first law postulates the existence of an inertial reference frame in which an object moves at constant velocity if the net force acting on it is zero. Consistent with Newtons third law of motion, the bullet pushes backwards upon the rifle. A gunpowder explosion creates hot gases that expand outward allowing the rifle to push forward on the bullet. This recoil is the result of action-reaction force pairs. They are the building blocks of Newtonian mechanics and if fewer were needed, Newton would simply formulate fewer. Many people are familiar with the fact that a rifle recoils when fired. Newton's laws of motion cannot be derived from each other. law of inertia, also called Newton’s first law, postulate in physics that, if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. The second law is just the definition of $F$, and the first law comes from noting that if you just have one body then $mv$ can't change, so $v$ has to be constant. If we define $F_1 = m_1 a_1$ and $F_2 = m_2 a_2$ then this becomes $F_1 = -F_2$, which is Newton's third law. One exerts a constant force on the other $F_(m_1v_1 + m_2v_2) = m_1a_1 + m_2a_2 = 0. The speed will remain constant and in a straight line in both scenarios. Imagine a universe with two bodies (with positions $x_1$ and $x_2$) of equal finite mass ($0< m_1=m_2 <\infty$). Watch on Newton’s First Law: Inertia An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force. Newton’s Laws of Motion is defined by including three crucial laws, which are: Unless an unbalanced force acts on an object, an object will continue remaining at rest if it is already at rest, and it will continue moving in uniform motion if it is already in uniform motion. In particular, for each law there is a possible universe where one law fails and the other two hold. You cannot derive any of the laws from each other.
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