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?

Explanation:

Step1: Find the speed (constant of proportionality)

The speed $v=\frac{d}{t}$, where $d = 21$ meters and $t = 3$ seconds. So $v=\frac{21}{3}=7$ m/s.

Step2: Calculate distance for $t = 1\frac{1}{2}=\frac{3}{2}$ seconds

Using the formula $d=v\times t$, with $v = 7$ m/s and $t=\frac{3}{2}$ s, we get $d=7\times\frac{3}{2}=\frac{21}{2}=10.5$ m.

Step3: Calculate distance for $t = 6\frac{3}{10}=\frac{63}{10}$ seconds

Using $d = v\times t$, with $v = 7$ m/s and $t=\frac{63}{10}$ s, we get $d=7\times\frac{63}{10}=\frac{441}{10}=44.1$ m.

The completed table:

Time (sec)	Distance (m)
$1\frac{1}{2}$	10.5
$6\frac{3}{10}$	44.1

Step4: Find the constant of proportionality

The relationship between distance $d$ and time $t$ is $d=kt$ (direct - proportion). Since $d = 21$ m when $t = 3$ s, the constant of proportionality $k=\frac{d}{t}=\frac{21}{3}=7$. In this situation, the constant of proportionality 7 represents the speed of the bicycle in meters per second.

Answer:

Completed table:

Time (sec)	Distance (m)
$1\frac{1}{2}$	10.5
$6\frac{3}{10}$	44.1

Constant of proportionality: 7. It represents the speed of the bicycle in m/s.