Question

problems 9 - 10: a bicycle travels 21 meters in 3 seconds.

1. complete the table.
2. what is a constant of proportionality in this relationship?

what does this represent in the situation?
reflection

1. put a star next to a problem that looked more difficult than it really was.
2. use this space to ask a question or share something youre proud of.

Explanation:

Step1: Calculate the speed

The speed \(v=\frac{\text{Distance}}{\text{Time}}\). Given distance \(d = 21\) m and time \(t=3\) s, so \(v=\frac{21}{3}=7\) m/s.

Step2: Find the distance for \(t = 1\frac{1}{2}=\frac{3}{2}\) s

Using the formula \(d=v\times t\), substitute \(v = 7\) m/s and \(t=\frac{3}{2}\) s. Then \(d=7\times\frac{3}{2}=\frac{21}{2}=10.5\) m.

Step3: Find the time for \(d = 6\frac{3}{10}=\frac{63}{10}\) m

Using the formula \(t=\frac{d}{v}\), substitute \(d=\frac{63}{10}\) m and \(v = 7\) m/s. Then \(t=\frac{\frac{63}{10}}{7}=\frac{63}{10}\times\frac{1}{7}=\frac{9}{10}=0.9\) s.

Step4: Find the constant of proportionality

The relationship between distance \(d\) and time \(t\) is \(d = kt\) (where \(k\) is the constant of proportionality). Since \(v=\frac{d}{t}\), and \(v = 7\) m/s, the constant of proportionality \(k = 7\). It represents the speed of the bicycle.

Answer:

Time (sec)	Distance (m)
\(1\frac{1}{2}\)	\(10.5\)
\(0.9\)	\(6\frac{3}{10}\)

The constant of proportionality is \(7\), which represents the speed of the bicycle.