Step 1: Calculate Total Energy

At $x = 1.0$ m, the particle has:

• Kinetic Energy $K = 1.0$ J
• Potential Energy $U = 1.0$ J (from graph)

Total Mechanical Energy is conserved:

$$E = K + U = 2.0 \text{ J}$$

Step 2: Find Turning Point

The turning point occurs where velocity is zero ($K=0$). At this point, all energy is potential:

$$U(x) = E = 2.0 \text{ J}$$

Looking at the graph for $x > 1.0$, the line starts at $(2,0)$ and rises linearly. We can see it passes through $(6, 2)$. Thus, the potential energy reaches $2.0$ J at:

$$x = 6.0 \text{ m}$$