A block of mass 5 ~kg moves along the x -direction subject to the...

\mathrm{F}=-20\left(\mathrm{x}-\frac{1}{2}\right)=-20 \mathrm{X} \quad\left($\mathrm{X}=\mathrm{x}$-\frac{1}{2}\right)$\therefore$ Particle will perform SHM about $\mathrm{x}=\frac{1}{2}$ with $\omega=2 \mathrm{rad} / \mathrm{sec} \Rightarrow \mathrm{T}=\pi \mathrm{sec}$. $\therefore$ Phase covered in $t=\frac{\pi}{4}$ second $=90^{\circ}$. Given particle is at rest at $\mathrm{x}=1 \mathrm{~m} \Rightarrow \mathrm{x}=1$ is extreme position. $\therefore$ In $\frac{\pi}{4}$ sec, it will be at equilibrium $\therefore \mathrm{x}=0.5 \mathrm{~m}$ and momentum $=\mathrm{m} \omega \mathrm{A}=5 \times 2 \times 0.5=5 \mathrm{~kg} \mathrm{~m} / \mathrm{s}$ Direction will be towards -ve $\mathrm{x}$. Hence option (3)