A \(10-\mathrm{kg}\) cart is connected to a \(20-\mathrm{kg}\) cart by a relaxed spring of spring constant \(1000 \mathrm{~N} / \mathrm{m}\), and both carts are placed on a low-friction track. You push the \(10-\mathrm{kg}\) cart in the direction of the \(20-\mathrm{kg}\) cart with a constant force of \(10 \mathrm{~N}\).

(a) What is the acceleration of the center of mass of the two-cart system at any instant?

(b) What is the acceleration of each cart at the instant you begin to push?

(c) What is the acceleration of each cart when the spring has its maximum compression?