Question

A particle moves along the x-axis obeying the equation $x=t(t-1)(t-2)$, where $x$ is in meter and $t$ is in second. Find the displacement when the velocity of the particle is zero.

Answer 1

$v=0\Rightarrow 3t^2-6t+2=0$

$\Rightarrow t=\frac{6\pm \sqrt{6^2-4\times 3\times 2}}{6}=\frac{6\pm \sqrt{12}}{6}=1\pm dfrac1\sqrt{3}=\frac{\sqrt{3}\pm 1}{\sqrt{3}}s$

At $t=\frac{\sqrt{3}-1}{\sqrt{3}}s,x=\left(\frac{\sqrt{3}-1}{\sqrt{3}}\right)(\frac{\sqrt{3}-1}{\sqrt{3}}-1)(\frac{\sqrt{3}-1}{\sqrt{3}}-2)$

$=\frac{2}{3\sqrt{3}}m.$

and $t=\frac{\sqrt{3}+1}{\sqrt{3}}s.$

$x=\left(\frac{\sqrt{3}+1}{\sqrt{3}}\right)(\frac{\sqrt{3}+1}{\sqrt{3}}-1)(\frac{\sqrt{3}+1}{\sqrt{3}}-2)=\frac{-2}{3\sqrt{3}}m$