Answer
a) $3.067\times10^3\;\rm m/s$
b) $0.223\;\rm m/s^2$
Work Step by Step
We know that the Earth completes one full revolution around its axis every 24 hours. This is also the rate of geosynchronous orbit satellites.
a)
Thus, the speed of the satellite is given by
$$v=\dfrac{S}{T}=\dfrac{2\pi r}{T}$$
whereas $T=24\;\rm h$ and $r=R_E+h$
$$v =\dfrac{2\pi (R_E+h)}{T}=\dfrac{2\pi ([6.37\times10^6]+[3.58\times10^7])}{24\cdot 60^2}$$
$$v=\color{red}{\bf 3.067\times10^3}\;\rm m/s$$
b)
We know that the acceleration of a geosynchronous satellite is a centripetal acceleration which is given by
$$a_r=\dfrac{v^2}{r}=\dfrac{v^2}{R_E+h}$$
$$a_r=\dfrac{(3.067\times10^3)^2}{[6.37\times10^6]+[3.58\times10^7]}=\color{red}{\bf 0.223}\;\rm m/s^2$$
