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Two cars are traveling with initial velocity V0 in the same direction, with some initial spacing...

Two cars are traveling with initial velocity V0 in the same direction, with some initial spacing d between them. The first car suddenly breaks to a halt. The car behind it also breaks after some time lag \Delta t, with the same deceleration.
1) Show the graph of distance versus time for both cars in the scenario
2) Show the graph of the minimum initial spacing d between the cars it takes for them to never touch after breaking versus time.
Explain in detail the reasoning, and provide mathematical descriptions for the shapes of each graph.

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