Answer
Please see the work below.
Work Step by Step
We know that
$\omega=\frac{2\pi \frac{rad}{s}}{27days\times \frac{24hrs}{day}\times \frac{3600s}{hr}}=\times 10^{-6}\frac{rad}{s}$
$r=384.4Mm=3.844\times 10^8m$
$v=r\omega$
We plug in the known values to obtain:
$v=(3.844\times 10^8)(2.7\times 10^{-6}\frac{rad}{s})=1035.3\frac{m}{s}$
We also know that
$a=\frac{v^2}{r}$
We plug in the known values to obtain:
$a=\frac{(1035.3)^2}{3.844\times 10^8}$
$a=2.8\times 10^{-3}\frac{m}{s^2}$
