Chapter 8.1, Problem 32E

To determine

Whether the given statement is True or False.

Answer to Problem 32E

The given statement is True.

Explanation of Solution

Given information:

If the velocity of a particle moving along the x-axis is always positive, then the displacement is equal to the total distance travelled.

If the velocity $v\left(t\right)$ of a particle is positive over the x-axis. Then it is clear that,

  ${\displaystyle \underset{0}{\overset{\infty }{\int }}v\left(t\right)}dt={\displaystyle \underset{0}{\overset{\infty }{\int }}\left|v\left(t\right)\right|}dt$

Which indicates that the displacement is equal to the total distance travelled.

Therefore, the given statement is True.