Chapter 7.1, Problem 14E

To determine

To find: The position of the particle at times $a$ , $b$ and $c$ .

Answer to Problem 14E

The position of the particle at times $a$ , $b$ and $c$ are 11 cm, 16 cm and $-8$ cm respectively.

Explanation of Solution

Given information:

The graph of velocity of the particle is given.

Calculation:

The graph is below the $t$ -axis between $t=0$ and $t=a$ . So, the area is negative.

The area under the curve between $t=a$ to $t=b$ is positive as it lies above the $t$ -axis. Again, the area from $t=b$ to $t=c$ is negative.

Find the position of the particle at $t=a$ .

  $\begin{array}{c}\text{Final position}=\text{Initial position }+\text{ displacement }\left(\text{from }t=0\text{ to }t=a\right)\\ =15+\left(-4\right)\\ =11\end{array}$

Therefore, the position of the particle at $t=a$ is 11 cm.

Find the position of the particle at $t=b$ .

  $\begin{array}{c}\text{Final position}=\text{Initial position }+\text{ displacement }\left(\text{from }t=0\text{ to }t=b\right)\\ =15+\left(-4\right)+5\\ =16\end{array}$

Therefore, the position of the particle at $t=b$ is 16 cm.

Find the position of the particle at $t=c$ .

  $\begin{array}{c}\text{Final position}=\text{Initial position }+\text{ displacement }\left(\text{from }t=0\text{ to }t=c\right)\\ =15+\left(-4\right)+5+\left(-24\right)\\ =-8\end{array}$

Therefore, the position of the particle at $t=c$ is $-8$ cm.

Conclusion:

The position of the particle at times $a$ , $b$ and $c$ are 11 cm, 16 cm and $-8$ cm respectively.