Block $\mathrm{A} \mathrm{and} \mathrm{C}$ start from rest and move to the right with acceleration ${\mathrm{a}}_{\mathrm{A}}=12\mathrm{tm}/{\mathrm{s}}^2$ and ${\mathrm{a}}_C=3 \mathrm{m}/{\mathrm{s}}^2$. Here $t$ is in seconds. The time when block $\mathrm{B}$ attain comes to rest is

From constraint relation we can see that acceleration of block $\mathrm{B}$ is ${\mathrm{a}}_B=\left(\frac{{\mathrm{a}}_A+{\mathrm{a}}_C}{2}\right)$ with proper signs. Hence ${\mathrm{a}}_{\mathrm{B}}=\left(\frac{3-12\mathrm{t}}{2}\right)=1.5-6\mathrm{t}$ or $\frac{{\mathrm{dv}}_{\mathrm{B}}}{\mathrm{dt}}=1.5-6\mathrm{t}$ or ${\int }_0^{{\mathrm{v}}_{\mathrm{B}}}{\mathrm{dv}}_{\mathrm{B}}={\int }_0^{\mathrm{t}}(1.5-6\mathrm{t})\mathrm{dt}$ or ${\mathrm{v}}_{\mathrm{B}}=1.5\mathrm{t}-3{\mathrm{t}}^2$ or ${\mathrm{v}}_{\mathrm{B}}=0$ at $\mathrm{t}=\frac{1}{2} \mathrm{s}$.