**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 m_{1} and m_{2} collide with each other and forces acting on these particles are only the ones they exert on each other.

•Let u_{1} and v_{1} be the initial and final velocities of particle A and similarly, u_{2} and v_{2 }for particle B. Let the two particles be in contact for a time t.

So, Change in momentum of A = m_{1} (v_{1}-u_{1}) Change in the momentum of B = m_{2} (v_{2}-u_{2})

•During the collision, let A impart an average force equal to F_{BA} on B and let B exert an average F_{AB }on A.

We know that from third law of motion F_{BA} = F_{AB} eq. (4)

F_{BA} = m_{2} x a_{2} = \(\frac{m_2(v_2-u_2)}{t}\)

F_{AB} = m_{1} x a_{1} = \(\frac{m_1(v_1-u_1)}{t}\)

Canceling t on both sides and rearranging the equation we get m_{1} u_{1 }+ m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2} eq.(5)

Now, m_{1} u_{1} + m_{2} u_{2} represents the total momentum of particles A and B before collision and m_{1} v_{1} + m_{2} v_{2} represents the total momentum of particles after the collision. This means that

Total momentum before collision = total momentum after the collision

**•Equation 5 which m**_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}, is known as the law of conservation of momentum.