Answer
Please see the work below.
Work Step by Step
We know that
$v(t)=\int a(t)(\frac{d}{dt})=\frac{1}{3}bt^3$
$s(t)=\int v(t)(\frac{d}{dt})=\frac{1}{12}bt^4$
$s(6.3)=5.38m$
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