Two \(0.50-\mathrm{kg}\) carts, one red and one green, sit about half a meter apart on a low-friction track. You push on the red one with a constant force of \(2.0 \mathrm{~N}\) for \(0.15 \mathrm{~m}\) and then remove your hand. The cart moves \(0.35 \mathrm{~m}\) on the track and then strikes the green 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 red cart?

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