Chapter 8.1, Problem 12E

To determine

To calculate: the particle’s displacement between $t=0$ and $t=c$ .

Answer to Problem 12E

The particle’s displacement between $t=0$ and $t=c$ is $-23$ cm

Explanation of Solution

Given information:

The figure shows the graph of velocity $v\left(t\right)$ .

Initial position of the particle at $t=0$ is $x\left(0\right)=15$ .the numbers shown in the graph are the areas of the enclosed region.

Calculation:

From the graph it is clear that it shows the characteristic of velocity with respect to time. And area under velocity time curve represents the distance.

As displacement is a vector quantity, the area enclosed when velocity is negative provides negative displacement.

  $\begin{array}{l}\text{displacement}=-4+5-24\\ =-23\end{array}$

Therefore,

The net displacement is $-23$ cm