Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 38_M

Figure 8.32 shows a plot of potential energy \(U\) versus position \(x\) of a \(0.200\text{ kg}\) particle that can travel only along an \(x\) axis under the influence of a conservative force. The graph has these values: \(U_A = 9.00\text{ J}\), \(U_C = 20.00\text{ J}\), and \(U_D = 24.00\text{ J}\). The particle is released at the point where \(U\) forms a “potential hill” of “height” \(U_B = 12.00\text{ J}\), with kinetic energy \(4.00\text{ J}\). What is the speed of the particle at (a) \(x = 3.5\text{ m}\) and (b) \(x = 6.5\text{ m}\)? What is the position of the turning point on (c) the right side and (d) the left side?