define newton 's third law of …

Newton’s Third Law of Motion states that there is always reaction for every action in opposite direction and of equal magnitude.
Explanation: Whenever a force is applied over a body, that body also applies same force of equal magnitude and in opposite direction.
Law of Conservation of Momentum – The sum of momenta of two objects remains same even after collision.
In other words, the sum of momenta of two objects before collision and sum of momenta of two objects after collision are equal.
Suppose that, two objects A and B are moving along a straight line in same direction and the velocity of A is greater than the velocity of B.
Let the initial velocity of A=u₁
Let the initial velocity of B= u₂
Let the mass of A = m₁
Let the mass of B = m₂
Let both the objects collide after some time and collision lasts for ' t' second.
Let the velocity of A after collision= v₁
Let the velocity of B after collision= v₂
We know that, Momentum = Mass x Velocity
Therefore, Momentum of A(FA) before collision =m₁×u₁
Momentum of B(FB) before collision =m₂×u₂
Momentum of A after collision = m₁×v₁
Momentum of B after collision = m₂×v₂
Now, we know that Rate of change of momentum
= Mass x rate of change in velocity
= mass x Change in velocity/time

Therefore, rate of change of momentum of A during collision, F_AB= {tex}m_1\left(\frac{v_1-u_1}t\right){/tex}
Similarly the rate of change of momentum of B during collision, F_BA= {tex}m_2\left(\frac{v_2-u_2}t\right){/tex}
Since, according to the Newton's Third Law of Motion, action of the object A (force exerted by A) will be equal to reaction of the object B(force exerted by B). But the force exerted in the course of action and reaction is in opposite direction.
Therefore, F_AB= −F_BA
{tex}m_1\left(\frac{v_1-u_1}t\right){/tex} = − {tex}m_2\left(\frac{v_2-u_2}t\right){/tex}
⇒m₁(v₁−u₁) =−m₂(v₂−u₂)

⇒m₁v₁−m₁u₁ =−m₂v₂+m₂u₂

⇒m₁v₁+m₂v₂  =m₁u₁+m₂u₂

⇒m₁u₁+m₂u₂ =m₁v₁+m₂v₂ ---(i)