Chapter 8.1, Problem 14E

To determine

To give the positions of the particle at times a, b, c.

Answer to Problem 14E

The position of particle at times a, b and c is 11, 16 and $-8$ .

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 position of a particle on the x axis is a vector quantity, the area enclosed when velocity is negative provides negative displacement.

  $\begin{array}{l}\text{position at }\left(t=a\right)=15-4\left[x\left(0\right)=15\right]\\ =11\\ \text{position at }\left(t=b\right)=15-4+5\left[x\left(0\right)=15\right]\\ =16\\ \text{position at }\left(t=c\right)=15-4+5-24\left[x\left(0\right)=15\right]\\ =-8\end{array}$

Therefore,

The position of particle at times a, b and c is 11, 16 and $-8$ .