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A particle is executing circular motion with a constant angular frequency of $=4\mathrm{.}33ra\frac{d}{s}.$ If time $t=0$ corresponds to the position of the particle being located at $y=0$ and $x=4\mathrm{.}7m,$ answer the following. $($Express your answers in vector form.$)$

$($a$)$ What is the position of the particle $($in m $)$ at $t=16s?$

vec$(r)=$ m

$($b$)$ What is its velocity $($in $\frac{m}{s})$ at this time?

vec$(v)=\frac{m}{s}$

$($c$)$ What is its acceleration $($in $\frac{m}{s^2})$ at this time?

vec$(a)=\frac{m}{s^2}$