Answer:
[tex]v = \frac{1}{5}\cdot s[/tex]
Explanation:
If the distance ([tex]s[/tex]) and speed ([tex]v[/tex]), measured in centimeters and centimeters per hour, respectively, are directly proportional to each other, then each set of values must observe the following relationship:
[tex]k = \frac{v}{s}[/tex] (Eq. 1)
Where [tex]k[/tex] is the proportionality constant, measured in [tex]\frac{1}{h}[/tex].
If we know that [tex]s_{1} = 10\,cm[/tex], [tex]v_{1} = 1\,\frac{cm}{h}[/tex], [tex]s_{2} = 15\,cm[/tex], [tex]v_{2} = 2\,\frac{cm}{h}[/tex], [tex]s_{3} = 15\,cm[/tex] and [tex]v_{3} = 3\,\frac{cm}{h}[/tex], then the constant of proportionality for each pair is:
[tex]k_{1} = \frac{v_{1}}{s_{1}}[/tex]
[tex]k_{1} = \frac{1\,\frac{cm}{h} }{5\,cm}[/tex]
[tex]k_{1} = \frac{1}{5}\,\frac{1}{h}[/tex]
[tex]k_{2} = \frac{v_{2}}{s_{2}}[/tex]
[tex]k_{2} = \frac{2\,\frac{cm}{h} }{10\,cm}[/tex]
[tex]k_{2} = \frac{1}{5}\,\frac{1}{h}[/tex]
[tex]k_{3} = \frac{v_{3}}{s_{3}}[/tex]
[tex]k_{3} = \frac{3\,\frac{cm}{h} }{15\,cm}[/tex]
[tex]k_{3} = \frac{1}{5}\,\frac{1}{h}[/tex]
As [tex]k_{1} = k_{2} = k_{3}[/tex], we conclude that correct equation is [tex]v = \frac{1}{5}\cdot s[/tex].
The correct equation that correctly state the relationship between the dot distances and speeds is ; S = 5 * V or [tex]V = 1 / 5 * s[/tex]
Although some data related to your question is missing a general answer within the scope of your question is provided
From the given data
The distance of the dot is directly proportional to the speed ( v ) of the dot
i.e. S ∝ V
∴ S = kV
K = S / V . -------- ( 1 )
where ;
S = distance of dot , V = speed of dot and K = proportionality constant.
Applying equation ( 1 ) to all three dot distances
K = 5 cm / 1 cm/hr = 5
K = 10 cm / 2 cm/hr = 5
K = 15 cm / 3 cm/hr = 5
Therefore we can conclude that the equation that will currently state the relationship between the dot distances and their speeds is [tex]V = 1 / 5 * s[/tex]
Learn more : https://brainly.com/question/23331901
