Two \(0.50-\mathrm{kg}\) carts are pushed toward each other from starting positions at cither end of a \(6.0-\mathrm{m}\) low-friction track. Each cart is pushed with a force of \(3.0 \mathrm{~N}\), and that force is exerted for a distance of \(1.0 \mathrm{~m}\).

(a) What is the work done on the two-cart system?

(b) What is the change in kinetic energy of the system?

(c) What is the kinetic energy of the center of mass of the system?