State Newton’s law of motion and use them to derive the law of conservation of momentum.

Newton’s laws of motion

• A body continues in its state of rest or uniform motion in a straight line unless acted upon by an external force
• The rate of change of momentum of a body is directly proportional to applied force and takes place in the direction of the force
• For every action, there is an equal and opposite reaction

Derivation of the law of conservation of momentum

Let m₁, m₂ be the masses of two bodies initially moving in the same direction with velocities u₁ and u₂  which collide after time t, and gain velocities v₁ and v₂ respectively when u₁ > u₂.

During collision, each body exerts a force of impact on each other according to Newton’s second law of motion.

Let I be the I impulse on A, then the impulse on B = -I.

I = M₁v₁ –m₁u₁ …………….. (i)

-I= m₂v₂ – m₂u₂ …………….. (ii)

Equation (i) + equation  (ii)

0 = M₁v₁ –m₁u₁+ m₂v₂ – m₂u₂

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Alternatively

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