Chapter 8.1, Problem 13E

To determine

To calculate: the total distance travelled by the particle between $t=0$ and $t=c$ .

Answer to Problem 13E

The particle’s total distance travelled between $t=0$ and $t=c$ is $33$ 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 distance travelled is a scalar quantity, it is the summation of all area enclosed by the curve whether velocity is positive or negative.

  $\begin{array}{l}\text{distance travelled}=4+5+24\\ =33\end{array}$

Therefore,

The total distance travelled is $33$ cm