Given below is the plot of potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that E_mech = 8J, the incorrect statement for this system is:

[Where KE = Kinetic Energy]

${\mathrm{E}}_{\mathrm{mech}}=8\mathrm{J}$

$\Rightarrow \mathrm{U}+\mathrm{K} = 8\mathrm{J}$

$$\begin{gathered} \mathrm{A}) \mathrm{x}={\mathrm{x}}_2\Rightarrow \\ \mathrm{U}=0 \& {\mathrm{E}}_{\mathrm{mech}}=\mathrm{K}=8\mathrm{J} \end{gathered}$$

KE is greatest and particle is moving at fastest speed.

$$\begin{gathered} \mathrm{B}) \mathrm{at} \mathrm{x}<{\mathrm{x}}_1, \\ \mathrm{U}=\mathrm{constant}=8\mathrm{J} \& \mathrm{K}={\mathrm{E}}_{\mathrm{mech}}-\mathrm{U}=8-8=0\mathrm{J} \end{gathered}$$

particle is at rest.

$$\begin{gathered} \mathrm{C}) \mathrm{At} \mathrm{x}={\mathrm{x}}_3, \mathrm{U}=4\mathrm{J} \\ \Rightarrow \mathrm{U}+\mathrm{K}=8\mathrm{J} \& \mathrm{K}=4\mathrm{J} \end{gathered}$$

$\mathrm{D}) \mathrm{at} \mathrm{x}>{\mathrm{x}}_4, \mathrm{U}=\mathrm{constant}=6\mathrm{J}\Rightarrow \mathrm{K}={\mathrm{E}}_{\mathrm{mech}}-\mathrm{U}=2\mathrm{J}=\mathrm{constant}$

Hence the incorrect statement is : at x < x₁, K.E is smallest and the particle is moving at the slowest speed.