I would know how much is the mobility rate of a DNA or protein strand across an electrophoretic gel when subjected to an electric field. Is there some indication about such rate indicated as nm/s, um/s or something like that? Thanks.
This gets really complicated as this is dependent upon temperature (=gel buffer volume), buffer type, DNA conformation, agarose concentration, loading buffer composition .... you get the idea.
If you are interested in a theoretical approach try: Migration of DNA molecules through entropic trap arrays: a dissipative particle dynamics study by E. Moeendarbary et al.
I personally would run the gel on your experimental setup and make a photo every 5 minutes and then try to reproduce it. This gives you an estimate for your setup. Be careful though, there are many pitfalls: the buffer volume changes due to evaporation (=more salts, less water, more heating ...), the agarose concentration changes evertyime you heat it up (evaporation), the quality of DNA might be not constant because photometric measurements are not very accurate (can not detect if one double strand or broken into many pieces).
Although some programs have estimative algorithms, the practical error rate is 5-10%.
If you want to cut the gel without UV exposure simply run 2 lanes next to each other and cover one of them. If the quantity is the same, they should run at the same speed.