<Dd> F + u d m d t = m d v d t (\ displaystyle \ mathbf (F) + \ mathbf (u) (\ frac (\ mathrm (d) m) (\ mathrm (d) t)) = m (\ mathrm (d) \ mathbf (v) \ over \ mathrm (d) t)) </Dd> <P> where u is the velocity of the escaping or incoming mass relative to the body . From this equation one can derive the equation of motion for a varying mass system, for example, the Tsiolkovsky rocket equation . Under some conventions, the quantity u dm / dt on the left - hand side, which represents the advection of momentum, is defined as a force (the force exerted on the body by the changing mass, such as rocket exhaust) and is included in the quantity F. Then, by substituting the definition of acceleration, the equation becomes F = ma . </P> <P> The third law states that all forces between two objects exist in equal magnitude and opposite direction: if one object A exerts a force F on a second object B, then B simultaneously exerts a force F on A, and the two forces are equal in magnitude and opposite in direction: F = − F. The third law means that all forces are interactions between different bodies, or different regions within one body, and thus that there is no such thing as a force that is not accompanied by an equal and opposite force . In some situations, the magnitude and direction of the forces are determined entirely by one of the two bodies, say Body A; the force exerted by Body A on Body B is called the "action", and the force exerted by Body B on Body A is called the "reaction". This law is sometimes referred to as the action - reaction law, with F called the "action" and F the "reaction". In other situations the magnitude and directions of the forces are determined jointly by both bodies and it isn't necessary to identify one force as the "action" and the other as the "reaction". The action and the reaction are simultaneous, and it does not matter which is called the action and which is called reaction; both forces are part of a single interaction, and neither force exists without the other . </P> <P> The two forces in Newton's third law are of the same type (e.g., if the road exerts a forward frictional force on an accelerating car's tires, then it is also a frictional force that Newton's third law predicts for the tires pushing backward on the road). </P>

What is the formula for newton 3rd law
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