PROBLEM:

Find the following for path D in the figure:

(a) The distance traveled.

(b) The magnitude of the displacement from start to finish.

(c) The displacement from start to finish. 

SOLUTION:

Part A

The position of D started from 9 m, then went to 3 m, and then went back to 5 m. The distance traveled by D is the sum of all the paths

\text{distance}=6\:\text{m}+2\:\text{m}=8\:\text{m}\ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)

Part B

The magnitude of the displacement is the difference between the final position and the initial position WITHOUT regard to sign

\left|\Delta x\right|=\left|9\:\text{m}-5\:\text{m}\right|=4\:\text{m} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)

Part C

The displacement is the difference between the final position and the initial position TAKING INTO ACCOUNT the sign

\Delta x=5\:\text{m}-9\:\text{m}=-4\:\text{m} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)