Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 82

For the arrangement of forces in Problem 81, a 2.00 kg particle is released at \( x = 5.00 \text{ m} \) with an initial velocity of \( 3.45 \text{ m/s} \) in the negative direction of the \( x \) axis. (a) If the particle can reach \( x = 0 \text{ m} \), what is its speed there, and if it cannot, what is its turning point? Suppose, instead, the particle is headed in the positive \( x \) direction when it is released at \( x = 5.00 \text{ m} \) at speed \( 3.45 \text{ m/s} \). (b) If the particle can reach \( x = 13.0 \text{ m} \), what is its speed there, and if it cannot, what is its turning point?