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## Answers

For example, take a system of two balls of mass M and m moving with velocity V and v respectively in a straight line. The total momentum of the system is (MV+mv). Let the two balls collide with each other and their final velocities becomes V₁ and v₁. After the collision, the momentum of the system is (MV₁+mv₁). Then, according to the principle of the conservation of linear momentum, (MV+mv = MV₁+mv₁)

(i)When the force F₁ of the truck acts on the car for a time t,then the velocity of car changes from u₂ to v₂. So,

Acceleration of the car, a₂=(v₂-u₂)/t

But force=mass x acceleration, so the force F₁ exerted by the truck on the car is given by:

F₁=m₂ x (v₂-u₂)/t..................(1)

(i)When the force F₂ of the car acts on the truck for a time t,then the velocity of car changes from u₁ to v₁. So,

Acceleration of the car, a₁=(v₁-u₁)/t

But force=mass x acceleration, so the force F₂ exerted by the truck on the car is given by:

F₂=m₁ x (v₁-u₁)/t...................(2)

Now the force F₁ exerted by the truck is the áction'and the force F₂ exerted by the car is the 'reaction'. But according to Newton's third law of motion, the action and the reaction are equal and opposite. That is,

F₁=-F₂

Now putting the values of F₁ and F₂ from equations (1) and (2) we get :

m₂(v₂-u₂)/t=-m₁(v₁-u₁)/t

Cancelling t from both the sides we get,

m₂(v₂-u₂)=-m₁(v₁-u₁)

m₂v₂-m₂u₂=-m₁v₁+m₁u₁

m₂v₂+m₁v₁=m₂u₂+m₁u₁

Now, m₂u₂+m₁u₁ represents the total speed of the car and the truck before the collisions whereas m₂v₂+m₁v₁ represents the total momentum after the collision of the truck and the car. This means that:

Total momentum after the collision=Total momentum before the collision

This is known as the principle of conservation of linear momentum.