How to Find Final Velocities in an Elastic Collision?

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To find the final velocities in an elastic collision involving two carts with given masses and spring potential energy, the conservation of energy and momentum principles are essential. The spring potential energy can be converted into kinetic energy when the carts are pushed apart. The equation for kinetic energy, Ek = 0.5 * m * V^2, can be used to solve for final velocities without needing the spring constant or displacement. The discussion highlights the importance of equating the spring energy to the kinetic energy of the carts to find their velocities. The approach taken appears valid, focusing on energy conservation rather than momentum directly.
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Mass of cart A: 1kg
Mass of Cart B: 3Kg
Spring potential energy: 24 Joules
Two carts are pushed apart when the spring is released.
Thats all the given and I'm suppose to find the final velocity.

I have no idea how to get started.
For me to use Es=(1/2)K*DeltaX^2, i don't have delta x or spring konstant.
For me to use P=M*V, Mass is not give and i don't know the momentum.
The only other equation i have i think that is related to this topic is the impulse equation. F*deltaT= Impulse
 
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When i drew the momentum bar graph, i set spring as the impulse so there was no momentum in beging but some at the end.
 
Now i figured out using lol diagram that es would be equal to ek so then Ek=.5*m*V^2 and found the velocity not using the momentum. Anyone think what i did was wrong?
 

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