A \(1.0-\mathrm{kg}\) cart and a \(0.50-\mathrm{kg}\) cart sit at different positions on a low-friction track. You push on the \(1.0-\mathrm{kg}\) cart with a constant \(2.0-\mathrm{N}\) force for \(0.15 \mathrm{~m}\). You then remove your hand, and the cart slides \(0.35 \mathrm{~m}\) and strikes the \(0.50-\mathrm{kg}\) cart.

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

(b) How far does the system's center of mass move while you are pushing the \(1.0-\mathrm{kg}\) cart?

(c) By what amount does your force change the kinetic energy of the system's center of mass?