Answer
K = 9.00 J
Work Step by Step
According to the graph, to get to x = 2.00 m from x = 5.00 m, the particle would have been acted on by $F_{2}$ = 5.00 N from x = 3.00 m to x = 2.00 m (which is a displacement d = –1.00 m). Thus, this force does a work W = $F_{2}$*d = (5.00 N)(–1.00m) = –5.0 J. The negative work makes sense because the force is acting opposite the displacement, slowing down the particle. This Work represents the change in kinetic energy. Therefore, since the particle had K = 14.0 J at x = 5.00 m: At x = 2.00 m, K = 14.0 J + (–5.00 J) = 9.00 J.
