Chapter 7.1, Problem 38E

To determine

To find: It needs to be determined whether the statement that the displacement for the particle is equal to the total distance traveled is true or false.

Answer to Problem 38E

The statement that the displacement for the particle is equal to the total distance traveled is true.

Explanation of Solution

Given information: A figure is shown in the textbook which shows the velocity for a particle moving along the x -axis is always positive.

It is known that a particle’s displacement between $t=a$ and $t=b$ is given by ${\displaystyle \underset{a}{\overset{b}{\int }}v\left(t\right)dt}$ and the total distance traveled is given as ${\displaystyle \underset{a}{\overset{b}{\int }}\left|v\left(t\right)\right|dt}$ .

As it is given that the velocity is always positive along the x -axis so one has ${\displaystyle \underset{a}{\overset{b}{\int }}\left|v\left(t\right)\right|dt}={\displaystyle \underset{a}{\overset{b}{\int }}v\left(t\right)dt}$ which means total distance traveled is equal to the displacement.

Hence the statement that the displacement for the particle is equal to the total distance traveled is true.