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It depends on the frictional forces and the masses. If the frictional forces were the same and the masses were equal, then the cart and the person on the skateboard would both move towards each other. If the mass of the cart were much bigger then the cart would move much less with the skateboarder moving most of the distance, if the cart were very light, then the skateboarder would move very little and the cart would move most of the distance.

A higher frictional force in either of the two and the movement would be less for that system.

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Q: What would happen if a person was on a skateboard and that person pulled a cart by a cord?
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