Halliday, Resnick & Walker — Kinetic Energy and Work: Problem 72

Work calculated by graphical integration. In Fig. 7.34b, an 8.0 kg block slides along a frictionless floor as a force acts on it, starting at \(x_1 = 0\) and ending at \(x_3 = 6.5 \text{ m}\). As the block moves, the magnitude and direction of the force vary according to the graph shown in Fig. 7.34a. For example, from \(x = 0\) to \(x = 1 \text{ m}\), the force is positive (in the positive direction of the \(x\) axis) and increases in magnitude from 0 to 40 N. And from \(x = 4 \text{ m}\) to \(x = 5 \text{ m}\), the force is negative and increases in magnitude from 0 to 20 N. The block’s kinetic energy at \(x_1\) is \(K_1 = 280 \text{ J}\). What is the block’s speed at (a) \(x_1 = 0\), (b) \(x_2 = 4.0 \text{ m}\), and (c) \(x_3 = 6.5 \text{ m}\)?