If you are not interested in relativistic effects, the answer to your question is easy to workout. According to Wikipedia, Alpha Centuri is 4.24 ly away (4.0114x$10^{16}\mathrm{m}$). So to get there in 60 yrs ($1892160000\mathrm{s}$).
So your non-relativistic answer is
$v = \frac{d}{t} = \frac{4.0114x10^{16}}{1892160000} = 21200000\mathrm{ms}^{-1}$.
This is 21200 $\mathrm{Kms}^{−1}$. The fastest recored space flight was 24,791Mph which is around 11$\mathrm{Kms}^{−1}$ which is 0.05% of 21200$\mathrm{Kms}^{−1}$. Note, I belive satalites in geostationary orbits do $\approx 17\mathrm{Kms}^{−1}$.
I hope this helps.