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# The position of a particle as a function of time is given by equation: $x =2t^3-6t^2+12t+6$. The acceleration of the body is zero at

$\begin{array}{1 1} t=1\;s \\ t=2\;s \\ t=3\;s \\t=0.5\;s \end{array}$

Answer :$t=1\;s$
$v= \large\frac{d}{dt} $$(x) =\large\frac{d}{dt}$$(2t^3)-\large\frac{d}{dt}$$(6t^2)+\large\frac{d}{dt}$$(12 t) $$+\large\frac{d}{dt}$$(6)$
$\quad= 6t^2-12 t+12$
$a= \large\frac{d}{dt}$$(v)= \large\frac{d}{dt}$$(6t^2)$$-\large\frac{d}{dt}$$(12 t) +\frac{d}{dt}$$(12)$
or $a = 12 t -12$
When $a=0, 12t-12=0$ or $t=1\;s$
edited Aug 13, 2014 by meena.p

+1 vote