Analogous to sex drive, which is your need or level of desire to have sex, homework drive is your level of desire or willingness to do homework at a particular time. Your homework drive can vary greatly, even over short periods of time. Let's say if when your homework drive is peaking you can bang out a 7-pager in a few hours, when your homework drive is low it could take you upwards of 10 hours to finish the same paper.
'C' Student: Dude, can you just let me copy your english homework when you finish... my homework drive is so low right now, there's no chance I do it myself.
'A' Student: Sure thing broski, I'll hit you up later. Just make sure you change the answers around a little bit.