Chapter 4, Problem 1Q

Figure 4-21 shows the path taken by a skunk foraging for trash food, from initial point i. The skunk took the same time T to go from each labeled point to the next along its path. Rank points a, b, and c according to the magnitude of the average velocity of the skunk to reach them from initial point i, greatest first.

Figure 4-21

To determine

To find:

The rank of points according to the magnitude of the average velocity of the skunk to reach them from initial point i.

Answer to Problem 1Q

Solution:

$\mathrm{R}\mathrm{a}\mathrm{n}\mathrm{k}:\mathrm{ }\mathrm{c}=\mathrm{a}>b$

Explanation of Solution

1) Concept:

Average velocity can be calculated by using displacement and time. Displacement is calculated by measuring change in position of object.

2) Formulae:

$\mathrm{A}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{ }\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}=\frac{\mathrm{D}\mathrm{i}\mathrm{s}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}}{\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{e}}$

3) Given:

i. $\mathrm{T}-\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{ }\mathrm{t}\mathrm{o}\mathrm{ }\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{ }\mathrm{b}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{ }\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{h}\mathrm{ }\mathrm{l}\mathrm{a}\mathrm{b}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{d}\mathrm{ }\mathrm{p}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t}.$

ii. $1\mathrm{ }\mathrm{b}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k}=1\mathrm{ }\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}.$

4) Calculations:

a) Point i to a:

$\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}=1\mathrm{b}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k}$

$\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{e}=1\mathrm{ }\mathrm{T}$

Hence,

$\mathrm{A}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{ }\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}=\frac{1}{\mathrm{T}}$

b) Point i to b:

$\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}=1\mathrm{ }\mathrm{b}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k}$

$\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{e}=2\mathrm{ }\mathrm{T}$

Hence,

$\mathrm{A}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{ }\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}=\frac{1}{2\mathrm{T}}$

c) Point I to c

$\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}=3\mathrm{ }\mathrm{b}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k}$

$\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{e}=3\mathrm{T}$

Hence,

$\mathrm{A}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{ }\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{i}\mathrm{t}\mathrm{y}=\frac{3}{3\mathrm{T}}=\frac{1}{\mathrm{T}}$

Therefore, from these three results we can say that, rank according to average velocity would be:

$\mathrm{R}\mathrm{a}\mathrm{n}\mathrm{k}:\mathrm{ }\mathrm{c}=\mathrm{a}>b$

Conclusion:

We know that displacement is a vector quantity and calculated by measuring the change in position of the object. We can calculate average velocity for each point by using displacement and time to reach there. And then we can rank them according to average velocity.