Two \(0.25-\mathrm{kg}\) carts, one red and one green, are stationary on a low-friction track. The carts are initially separated by \(0.50 \mathrm{~m}\). You push on the red one with a constant force of 1.5 \(\mathrm{N}\) toward the green one. When the carts meet, they join together, and you continue to push with the same constant force as the connected carts move a further \(0.75 \mathrm{~m}\) along the track, at which point you remove your hand.

(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 applying the force?

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