Answer
$s=285.3205253\text{ radians cm}$
Work Step by Step
RECALL:
(1) $v=r\omega$
(2) $v=\dfrac{s}{t}$
Substitute the given values of $r$ and $\omega$ into formula (1) above to obtain:
\begin{array}{ccc}
&v&=&r\omega
\\&v&= &(11.46\text{ cm})(4.283\text{ radians per sec})
\\&v&=&49.08318\text{ radians cm per sec}\end{array}
Substitute the answer above and the given value of $t$ into formula (2) above to obtain:
\begin{array}{ccc}
&v &= &\frac{s}{t}
\\&49.08318 \text{ radians cm per sec} &=&\dfrac{s}{5.813 \text{ sec}}\end{array}
Cross-multiply to otbain:
\begin{array}{ccc}
&s &= &(49.08318 \text{ radians cm per sec})(5.813 \text{ sec})
\\&s &=&285.3205253\text{ radians cm}\end{array}