Answer
The total energy $(11.9 \mathrm{J})$ is equal to the potential energy (in the scenario where it is initially moving rightward) at $x=10.9756 \approx 11.0 \mathrm{m} .$ This point may be found by interpolation or simply by using the work-kinetic energy theorem:
$$
K_{f}=K_{i}+W=0 \Rightarrow 11.9025+(-4) d=0 \quad \Rightarrow \quad d=2.9756 \approx 2.98
$$
(which when added to $x=8.00$ [the point where $F_{3}$ begins to act] gives the correct result). This provides a turning point for the particle's motion.
Work Step by Step
The total energy $(11.9 \mathrm{J})$ is equal to the potential energy (in the scenario where it is initially moving rightward) at $x=10.9756 \approx 11.0 \mathrm{m} .$ This point may be found by interpolation or simply by using the work-kinetic energy theorem:
$$
K_{f}=K_{i}+W=0 \Rightarrow 11.9025+(-4) d=0 \quad \Rightarrow \quad d=2.9756 \approx 2.98
$$
(which when added to $x=8.00$ [the point where $F_{3}$ begins to act] gives the correct result). This provides a turning point for the particle's motion.
