As I understand it, you wouldn't need to reach escape velocity in a space elevator. Think about it this way, if instead of an elevator, you have a space ladder

As I understand it, you wouldn't need to reach escape velocity in a space elevator. Think about it this way, if instead of an elevator, you have a space ladder, in theory (if you have unlimited energy) you could climb to whatever height you want, without reaching escape velocity. AFAIK escape velocity is the minimum required to "throw" something away from earth such as it would never come back because of gravity.