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If cart 1 with an initial velocity of v1 collides with cart 2 with initial velocity...

If cart 1 with an initial velocity of v1 collides with cart 2 with initial velocity v2, and after the collision, they move as a single mass. What would the graph of the center of mass vs time look like? (assume t = 0 is the moment right after the impulse to Cart 1 is delivered and assume equal masses)

What about if instead, they move as one mass, they are repelled by each other if there are magnetic bumpers present? What would the graph of the center of mass vs time look like in that case?

Please explain!!!

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