Chapter 2, Problem 23P

(a)

To determine

What is the chipmunk’s total displacement?

Answer to Problem 23P

The total displacement of chipmunk is $170\text{cm to the left}$.

Explanation of Solution

The chipmunk travels a distance of $x_1$ to his right, $x_2$ distance to the left, $x_3$ distance to the right, $x_4$ distance to the left.

Let us take right side to be positive and left side to be negative. The direction and distance travelled by chipmunk is shown in figure 1 below.

Write the equation to find the total displacement of chipmunk.

$d=x_1-x_2+x_3-x_4$ (I)

Here, $d$ is the total displacement, $x_1,x_2,x_3\text{and }{x}_4$ are the distances

Conclusion

Substitute $80\text{cm}$ for $x_1$ , $30\text{cm}$ for $x_2$ , $90\text{cm}$ for $x_3$ , $310\text{cm}$ for $x_4$ in equation (I) to get $d$.

$\begin{array}{c}d=80\text{cm}-30\text{cm+90}\text{cm}-310\text{cm}\\ \text{=}-\text{170}\text{cm}\end{array}$

Since the displacement is negative, its direction is towards the left.

Therefore, the total displacement of chipmunk is $170\text{cm}$ to the left.

(b)

To determine

What is the average speed of chipmunk in a time of $18\text{s}$ ?

Answer to Problem 23P

The average speed of chipmunk is $28\text{cm}/\text{s}$.

Explanation of Solution

Write the equation to find the total distance travelled by chipmunk.

$d=x_1+x_2+x_3+x_4$ (I)

Here, $d$ is the total distance, $x_1,x_2,x_3\text{and }{x}_4$ are the distances

Write the equation to find the average speed.

$v_{av}=\frac{d}{t}$ (II)

Here, $v_{av}$ is the average speed, $d$ is the total distance, $t$ is the tome

Conclusion:

Substitute $80\text{cm}$ for $x_1$ , $30\text{cm}$ for $x_2$ , $90\text{cm}$ for $x_3$ and $310\text{cm}$ for $x_4$ in equation (I) to get $d$.

$\begin{array}{c}d=80\text{cm+30}\text{cm+90}\text{cm+310}\text{cm}\\ \text{=510}\text{cm}\end{array}$

Substitute $510\text{cm}$ for $d$ and $18\text{s}$ for $t$ in equation (II) to get $v_{av}$

$\begin{array}{c}{v}_{av}=\frac{510\text{cm}}{18\text{s}}\\ =28\text{cm}/\text{s}\end{array}$

Therefore, The average speed of chipmunk is $28\text{cm}/\text{s}$.

(c)

To determine

What is the average velocity of chipmunk?

Answer to Problem 23P

The average velocity of chipmunk is $9.4\text{cm}/\text{s}\text{ to the left}$.

Explanation of Solution

Write the equation to find the total displacement by chipmunk.

$d=x_1-x_2+x_3-x_4$ (I)

Here, $d$ is the total displacement, $x_1,x_2,x_3\text{and }{x}_4$ are the distances

Write the equation to find the average speed.

$v_{av}=\frac{d}{t}$ (II)

Here, $v_{av}$ is the average speed, $d$ is the total distance, $t$ is the tome

Conclusion:

Substitute $80\text{cm}$ for $x_1$ , $30\text{cm}$ for $x_2$ , $90\text{cm}$ for $x_3$ and $310\text{cm}$ for $x_4$ in equation (I) to get $d$.

$\begin{array}{c}d=80\text{cm-30}\text{cm+90}\text{cm-310}\text{cm}\\ \text{=-170}\text{cm}\end{array}$

Substitute $-170\text{cm}$ for $d$ and $18\text{s}$ for $t$ in equation (II) to get $v_{av}$

$\begin{array}{c}{v}_{av}=\frac{-170\text{cm}}{18\text{s}}\\ =-9.4\text{cm}/\text{s}\end{array}$

Therefore, The average speed of chipmunk is $-9.4\text{cm}/\text{s}$.