Explain the law of conservation of …

Law of conservation of momentum states that : For two or more bodies in an isolated system acting upon each other, their total momentum remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed.

Newton’s third law states that for a force applied by an object A on object B, object B exerts back an equal force in magnitude, but opposite in direction. This idea was used by Newton to derive the law of conservation of momentum.

Consider two colliding particles A and B whose masses are m₁ and m₂ with initial and final velocities as u₁ and v₁ of A and u₂ and v₂ of B. The time of contact between two particles is given as t.

A=m₁(v₁−u₁) (change in momentum of particle A)

B=m₂(v₂−u₂) (change in momentum of particle B)

F_BA=−F_AB (from third law of motion)

F_BA=m₂∗a₂=m₂(v₂−u₂)/t

F_AB=m₁∗a₁=m₁(v₁−u₁)/t

m₂(v₂−u₂)/t=−m₁(v₁−u₁)/t