Question

A student leaving school travels 100 m East before he realizes he left his textbook in his locker. He heads back towards school, travels 30 m West, and then stops as he remembers he has a spare textbook at home. So he decides to just head home, walking 70 m East before he arrives at his front door. What is the... (a) overall distance (b) displacement ... of that student?

Answer 1

-- The overall distance he travels is (100m + 30m + 70m) = 200 meters.

-- His displacement when he arrives at his front door is

D = (100m East) + (30m West) + (70m East)

D = (100m + 70m)East + (30m)West

D = (170m East) + (30m West)

D = 140 meters East

It's interesting to notice that his displacement is 60 meters shorter than the distance he walked.  

That's because there's a stretch of 30 meters somewhere in the middle that he actually covered three times.

Two of those times added to the distance his shoes covered (2x30m=60m), but they cancelled out of the displacement.

His front door is 140 meters East of school.  He walked 60m farther than that, going back and forth over the 30m piece.