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Solve the all parts of given question:

Question: A 2.0-kg cart and a 3.0-kg cart collide on a low-friction track. The 3.0-kg cart is initially moving at 2.0m/s to the right, but after the collision it is moving at 6.5m/s to the right. After the collision, the 2.0-kg cart is moving to the right at 3.5m/s.

Part A: If the direction from left to right is positive, what was the 2.0-kg cart's initial velocity?

Part B: What would your answer be if, other quantities being unchanged, the 3.0-kg cart were initially moving to the left at 2.0m/s?

Please show all work and clearly explain each step.

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