Derive principle of conservation of momentum …

Suppose 2 bodies a truck and a car are moving with different velocities,let the mass of the truck be m1 and initial velocity be u1,so that its initial momentum is m1u1. Similarly let initial momentum of the car br m2u2.. Thus total momentum of trock and car before colloision will be m1u1+m2u2. Suppose the truck and the car collide for a short time t. Let the velocity of truck after collision be v1 and of the car be v2, so yhat their final momentums will be m1v1+m2v2. The force F1 of truck acts on the car is given by: F1=m2a2=m2(v2-u2)/t Then force of the car on truck is given by: F2=m1a1=m1(v1-u1)/t But according to Newton's third law of motion we have: F1=F2 m2(v2-u2)/t = -m1(v1-u1)/t m2v2-m2u2 = -(m1v1 - m1u1) m2v2+m1v1 =m1u1+m2u2 OR m1u1+m2u2 = m1v1+m2v2 Total momentum before collision = Total momentum after collision