A red \(10-\mathrm{kg}\) cart is connected to a \(20-\mathrm{kg}\) cart by a relaxed spring of spring constant \(60 \mathrm{~N} / \mathrm{m}\). The \(20-\mathrm{kg}\) cart is resting against another \(10-\mathrm{kg}\) cart, this one blue. All are on a low-friction track. You push the red \(10-\mathrm{kg}\) cart to the right, 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 three-cart system?

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

(c) What is the vector sum of the forces on each cart when the spring is compressed \(100 \mathrm{~mm}\) ?