College Physics Problem 2.4


Find the following for path D in the figure:

An x axis starts at 0 meters and ends at 12 meters. There are four points on the graph with displacement paths. Path A starts at 0 and stops at 7. Path B starts at 12 and ends at 7. Path C starts at 2, goes to 10, turns around and goes back to 8, then turns around again and stops at 11. Path D starts at 9, goes to 3, then turns around and stops at 5.

(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

\displaystyle \text{distance}=6\:\text{m}+2\:\text{m}=8\:\text{m}          ☚

Part b

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

\displaystyle \left|\Delta x\right|=\left|9\:\text{m}-5\:\text{m}\right|=4\:\text{m}          ☚

Part c

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

\displaystyle \:\Delta x=5\:\text{m}-9\:\text{m}=-4\:\text{m}          ☚