Behold Halliday's Question and Halliday's answers: The only force acting on a 2.0 kg body as it moves along the x axis varies as shown in Figure 7-41 (see attatchment). The velocity of the body at x = 0 is 4.0 m/s. (a) What is the kinetic energy of the body at x = 3.0 m? 12 J (b) At what value of x will the body have a kinetic energy of 8.0 J? 4.0 m (c) What is the maximum kinetic energy attained by the body between x = 0 and x = 5.0 m? 18 J I am stumped. I've only tried to figure out (a) and (b), but my method does not give me correct answers. My train of thought was that Delta KE=W=area under curve. So for part (a), I said that area under graph is (triangle-triangle-rectangle) = -4 Nm. Well, gee. Maybe since KE is always positive, take the absolute value of various areas! I think that is very poor reasoning, because Delta KE and W can both be negative. And even when I do that, I get 8 Nm, which is still wrong. Similar reasoning applied to (b) also gives the incorrect answer, which is comforting. A hint from the wise gurus perhaps?