jozzo1000,

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.

--Kevin C.