Serway & Jewett — Energy of a System: Problem 35.

A single conservative force acts on a 5.00-kg particle within a system due to its interaction with the rest of the system. The equation \( F_x = 2x + 4 \) describes the force, where \( F_x \) is in newtons and \( x \) is in meters. As the particle moves along the x axis from \( x = 1.00 \text{ m} \) to \( x = 5.00 \text{ m} \), calculate (a) the work done by this force on the particle, (b) the change in the potential energy of the system, and (c) the kinetic energy the particle has at \( x = 5.00 \text{ m} \) if its speed is \( 3.00 \text{ m/s} \) at \( x = 1.00 \text{ m} \).