Elastic & Inelastic Collisions

I know that there will be 2 solutions, 1 for before collision, and the other is at minimum separation. But I don't know which is which...neither 6m/s nor -2m/s matches the given information that at minimum separation, both are moving at +2m/s

 

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Careful. Is the total kinetic energy equal to 70.0625 J at the point of minimum separation? The two solutions are for when none of the energy is potential energy.

 

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Oh! So the correct answer is -2m/s for the 3 kg cart and 8m/s for the 2kg cart. And the 2m/s coming out as a solution has nothing to do with the 2m/s[E] at minimum separation...

6m/s and -4m/s actually represents the velocities of the two carts AFTER the collision.

What if the question didn't tell you anything about the initial directions of the carts? Will there be 2 different sets of answers that are both valid?

 

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You'd get the same two answers, but you wouldn't be able to tell which were the initial and which were the final velocities, based on the information given.