Which of these problems do you want help with?
(4) is a simple Galilean transform problem: velocities add linearly.
In (10), you use the fact that the potential energy U for a conservative force F is , or for a one-dimensional problem,
to obtain the potential energy U(x), and use the fact that the total energy
E=T+U is a constant (with the kinetic energy) to find the x where it comes to rest (where v=0 and thus T=0)
In (11), you use the fact that E=T+V, T being kinetic energy, along with the fact that T ≥ 0 to determine the motion qualitatively.