Question

Two children start at one end of a street, the origin, run to the other end, then head back. On the way back Joan is ahead of Mike. Which statement is correct about the distances run and the displacements from the origin?
a. Joan has run a greater distance and her displacement is greater than Mike's.
b. Mike has run a greater distance and his displacement is greater than Joan's.
c. Joan has run a greater distance, but her displacement is less than Mike's.
d. Mike has run a greater distance, but his displacement is less than Joan's.
e. Mike has run a shorter distance, and his displacement is less than Joan's.

Answer 1

Joan has run a greater distance, but her displacement is less than Mike's. (c)

Displacement is the distance from the start-point to the end-point.  Since they're on the way back, their displacement is getting smaller as they go.  

If Joan is ahead of Mike, then she's closer to the starting point.  Her displacement since they started is smaller, AND PLUS ... when they both get back to the starting point, their total displacements will both be zero !