Two carts, A, with mass m and B, with mass 2m, are placed on a frictionless horizontal track. They are connected by a massless spring with a spring constant k, which is initially compressed by an amount X from its natural length. The system is released from rest with the spring in its compressed state. Find the speeds of carts A and B when they no longer are in contact with the spring.

• A. $V_{A}=2 X \sqrt{\frac{k}{6 m}}, V_{B}=X \sqrt{\frac{k}{6 m}}$
• B. $V_{A}=X \sqrt{\frac{k}{6 m}}, V_{B}=2 X \sqrt{\frac{k}{6 m}}$
• C. $V_{A}=X \sqrt{\frac{k}{m}}, V_{B}=\frac{X \sqrt{\frac{k}{m}}}{2}$
• D. $V_{A}=X \sqrt{\frac{k}{3 m}}, V_{B}=X \sqrt{\frac{k}{12 m}}$

Answer: (A)