Hint 1

(a) $E(p)=\sqrt{m^2c^4+p^2c^2}$.

(b)The Taylor's series for $E(p)$ is

$$E(p)=mc^2\left(1+{p^2\over m^2c^2}\right)^{1/2} \simeq mc^2\left(1+{1\over 2}\,{p^2\over m^2 c^2}+\cdots\right).$$

(c) $E(v)=\gamma(v)mc^2$ where $\gamma(v)=1/\sqrt{1-{v^2/c^2}}$. Rearrange this to get $v$ in terms of $E$.