## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

(a) We know that $E = KE + PE$ KE is a maximum when PE is a minimum. PE is a minimum at x = 6, so KE is a maximum at x = 6. Therefore the speed is a maximum at x = 6. (b) The particle has a turning point at x = 2 and at x = 8. When PE = E, the kinetic energy KE is zero. The particle turns back to the left at x = 8 and the particle turns back to the right at x = 2. (c) If E = PE at a point where PE is at a local minimum (the bottom of a potential well), then the particle will stay at rest. If E is changed so that E = PE at x = 3, the particle could remain at rest at x = 3. If E is changed so that E = PE at x = 6, the particle could remain at rest at x = 6. The particle could remain at rest at x = 3 and x = 6.