A \(4.0-\mathrm{kg}\) block and a \(2.0-\mathrm{kg}\) block are connected to opposite ends of a relaxed spring of spring constant \(300 \mathrm{~N} / \mathrm{m}\). The blocks are pushed toward each other for \(0.50 \mathrm{~s}\). The \(4.0-\mathrm{kg}\) block is pushed with a force of \(50 \mathrm{~N}\), and the \(2.0-\mathrm{kg}\) block is pushed with a force of \(20 \mathrm{~N}\). Ignore the inertia of the spring.

(a) What is the acceleration of the center of mass of the two-block system while this pushing is going on?

(b) When the blocks are released, what is the velocity of the \(2.0-\mathrm{kg}\) block if the \(4.0-\mathrm{kg}\) block is moving away from it at \(5.0 \mathrm{~m} / \mathrm{s}\) in the Earth reference frame?