What exactly is path length? How is it different from displacement?
Imagine you are standing at the starting line of a running track. As you jog laps around the track, each time you cross the starting line your displacement is zero, but your pathlength keeps increasing as you keep jogging. If you nailed down one end of a spool of string on the starting line, then the length of string that unwound (assuming it fell directly to the ground behind you) would be the pathlength that you traveled during your workout. Pathlength is the integral of speed (the absolute value of velocity) with respect to time from the time that you started running, until you finished.