According to the law of conservation of momentum

When two or more bodies act upon each other their total momentum remains constant provided no external forces are acting

•So, Momentum is never created or destroyed.

•When this law is applied for a collision between two bodies, the total momentum of the colliding bodies before the collision is equal to the total momentum after the collision.

•We can apply this law for a collision between two vehicles. This law is applicable for all types of collisions.

•Consider two particles say A and B of mass m1 and m2 collide with each other and forces acting on these particles are only the ones they exert on each other.

•Let u₁ and v₁ be the initial and final velocities of particle A and similarly, u₂ and v₂for particle B. Let the two particles be in contact for a time t.

So, Change in momentum of A=m₁ (v₁-u₁) Change in the momentum of B=m₂ (v₂-u₂ )

•During the collision, let A impart an average force equal to F_BA on B and let B exert an average F_ABon A. We know that from third law of motion F_BA=F_AB eq.(4)
Here,

canceling t on both sides and rearranging the equation we get
m₁u₁+m₂u₂ = m₁v₁+m₂v₂ eq.(5)
Now, m₁u₁+m₂u₂ represents the total momentum of particles A and B before collision and m₁v₁+m₂v₂ represents the total momentum of particles after the collision. This means that
Total momentum before collision=total momentum after the collision

•Equation 5 which m₁u₁+m₂u₂ = m₁v₁+m₂v₂ ,is known as the law of conservation of momentum.