Question

The position of a particle varies according to expression $x=t\left(t-1\right)\left(t-2\right)$, velocity of the particle is zero at times.

• A. $\left(1-\frac{1}{\sqrt{3}}\right),0$
• B. $\left(1+\frac{1}{\sqrt{3}}\right),0$
• C. 0, 1
• D. $\left(1-\frac{1}{\sqrt{3}}\right),\left(1+\frac{1}{\sqrt{3}}\right)$

Answer 1

The correct option is D $\left(1-\frac{1}{\sqrt{3}}\right),\left(1+\frac{1}{\sqrt{3}}\right)$

$x=t^3-3t^2-t$

$v=\frac{dx}{dt}$

$v=3t^2-6t-1$

$v=0$

$t=\frac{6\pm \sqrt{36-4\times 3}}{6}$

$t=(1\pm \frac{1}{\sqrt{3}})$