Chapter 7.1, Problem 18E

a.

To determine

To find: The position of the particle at the end of the trip.

Answer to Problem 18E

The position of the particle at the end of the trip is $2\text{ m}$ .

Explanation of Solution

Given information:

The graph of the velocity of the particle is given.

Calculation:

The area under the curve from $t=0$ to $t=1$ is ${\text{1 m}}^2$ . Similarly, the area under the curves from $t=1$ to $t=2$ is $-{\text{1 m}}^2$ , from $t=2$ to $t=3$ is ${\text{1 m}}^2$ and $t=3$ to $t=4$ is $-{\text{1 m}}^2$ .

  $\begin{array}{c}\text{Displacement}=1+\left(-1\right)+1+\left(-1\right)\\ =0\end{array}$

Then,

  $\begin{array}{c}\text{Final position}=\text{Initial position }+\text{ displacement}\\ =2+0\\ =2\text{ m}\end{array}$

Conclusion:

The position of the particle at the end of the trip is $2\text{ m}$ .

b.

To determine

To find: The total distance traveled by the particle.

Answer to Problem 18E

The total distance traveled by the particle is $4\text{ m}$ .

Explanation of Solution

Given information:

The graph of the velocity of the particle is given.

Calculation:

The area under the curve from $t=0$ to $t=1$ is ${\text{1 m}}^2$ . Similarly, the area under the curves from $t=1$ to $t=2$ is $-{\text{1 m}}^2$ , from $t=2$ to $t=3$ is ${\text{1 m}}^2$ and $t=3$ to $t=4$ is $-{\text{1 m}}^2$ .

The total distance traveled is $\left|1\right|+\left|-1\right|+\left|1\right|+\left|-1\right|=4\text{ m}$ .

Conclusion:

The total distance traveled by the particle is $4\text{ m}$ .