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The initial-state final-state diagrams are most useful in collision problems or in problems solved by using the Mechanical Energy and Non-Conservative Work model. In the following figure we present the initial-state final-state diagram of a two cars -car collision. Before the collision, the car of mass m1 m₁ is at rest and the car of mass m₂ is moving to the right at speed v₂(t_before). After the collision, both cars are moving. The car of mass m₁ is moving to the right with speed v₁(t_after)_m and the car of mass _m₂ is moving to the left with speed v₂(t_after). The goal of the problem is to find the speed of the car of mass m1 before the collision.

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Step 1. Identify the system and indicate it with a circle. (In this problem we will consider the system to be both cars. The reason is that we will assume that the collision time is very short so the possible external forces exerted on the system will produce a negligible external impulse, so we can solve the problem by using that the linear moment momentum of the two-car system is constant).

Step 2. Identify the initial state of the system. (In this problem, the initial state is right before the collision when the car of mass
m₁ is at rest and the car of mass m₂ is moving to the right with speed v₂(t_before). )

Step 3. Identify the final state of the system. (In this problem, the final state is right after the collision when the car of mass m₁ is moving to the right at speed v₁(t_after), and the car of mass m₂ is moving to the left with speed v₂(t_after). )