College Physics Problem 2.2


Find the following for path B 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

Based from the figure, B travels from 12 to 7. The distance traveled is 5 meters.

Part b

The magnitude of the displacement is 5 meters.

Part c

The displacement is calculated keeping in mind the sign. The motion started from 12 and ended at 7. Therefore, the displacement is

\displaystyle \Delta x=7\:\text{m}-12\:\text{m}=-5\:\text{meters}