Chapter 7.1, Problem 20E

a.

To determine

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

Answer to Problem 20E

The position of the particle at the end of the trip is $6.5\text{ m}$ .

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 $t=2$ is ${\text{3 m}}^2$ , from $t=2$ to $t=7$ is $-{\text{12 m}}^2$ , from $t=7$ to $t=10$ is $\frac{9}{2}{\text{ m}}^2$ .

Therefore, $\text{Displacement}=3-12+\frac{9}{2}=-4.5$ .

Then,

  $\begin{array}{c}\text{Final position}=\text{Initial position }+\text{ displacement}\\ =2+4.5\\ =6.5\text{ m}\end{array}$

Conclusion:

The position of the particle at the end of the trip is $6.5\text{ m}$ .

b.

To determine

To find: The total distance traveled by the particle.

Answer to Problem 20E

The total distance traveled by the particle is $19.5\text{ m}$ .

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 $t=2$ is ${\text{3 m}}^2$ , from $t=2$ to $t=7$ is $-{\text{12 m}}^2$ , from $t=7$ to $t=10$ is $\frac{9}{2}{\text{ m}}^2$ .

The total distance traveled is $\left|3\right|+\left|-12\right|+\left|4.5\right|=19.5\text{ m}$ .

Conclusion:

The total distance traveled by the particle is $19.5\text{ m}$ .