A particle starts moving from time $t = 0$ and its coordinate is given as $x(t) = 4t^{3} - 3t$.A. Th

Question

A particle starts moving from time $t = 0$ and its coordinate is given as $x(t) = 4t^{3} - 3t$.

A. The particle returns to its original position (origin) 0.866 units later

B. The particle is 1 unit away from origin at its turning point.

C. Acceleration of the particle is non-negative.

D. The particle is 0.5 units away from origin at its turning point.

E. Particle never turns back as acceleration is non-negative.

Choose the correct answer from the options given below :

Accepted Answer

$x = 0 \Rightarrow t = 0,\frac{\sqrt{3}}{2}$$$v = 12t^{2} - 3 $$At turning point, $v = 0$$$t = \frac{1}{2} \Rightarrow x = \frac{4}{8} - \frac{3}{2} = - 1 $$$a = 24t$ (always positive)

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