\begin{tabular}{|c|c|c|c|}
\hline
& \begin{tabular}{c}
Cart Speed \\
(Low Fan \\
Speed) \\
(cm/s)
\end{tabular}
& \begin{tabular}{c}
Cart Speed \\
(Medium \\
Fan Speed) \\
(cm/s)
\end{tabular}
& \begin{tabular}{c}
Cart Speed \\
(High Fan \\
Speed) \\
(cm/s)
\end{tabular} \\
\hline
\begin{tabular}{c}
Elapsed \\
time to \\
finish line \\
(s)
\end{tabular}
& 7.4
& 6.4
& 5.6 \\
\hline
\begin{tabular}{c}
Total \\
distance \\
[tex]$(cm)$[/tex]
\end{tabular}
& 500
& 500
& 500 \\
\hline
\begin{tabular}{c}
Average \\
velocity \\
[tex]$(cm/s)$[/tex]
\end{tabular}
& [tex]$?$[/tex]
& [tex]$?$[/tex]
& [tex]$?$[/tex] \\
\hline
\end{tabular}

Calculate the average velocity of the cart for each fan speed. Round your answers to the nearest tenth.

The cart with Low fan speed has an average velocity of [tex]$\square$[/tex] [tex]$cm/s$[/tex].

The cart with Medium fan speed has an average velocity of [tex]$\square$[/tex] [tex]$cm/s$[/tex].

The cart with High fan speed has an average velocity of [tex]$\square$[/tex] [tex]$cm/s$[/tex].



Answer :

To solve for the average velocity of the cart for each fan speed, we use the formula for average velocity:

[tex]\[ \text{Average Velocity} = \frac{\text{Total Distance}}{\text{Elapsed Time}} \][/tex]

Step-by-step Solution:

1. For Low Fan Speed:

- Total Distance (D): 500 cm
- Elapsed Time (T): 7.4 seconds

[tex]\[ \text{Average Velocity} = \frac{500 \text{ cm}}{7.4 \text{ s}} \approx 67.6 \text{ cm/s} \][/tex]

2. For Medium Fan Speed:

- Total Distance (D): 500 cm
- Elapsed Time (T): 6.4 seconds

[tex]\[ \text{Average Velocity} = \frac{500 \text{ cm}}{6.4 \text{ s}} \approx 78.1 \text{ cm/s} \][/tex]

3. For High Fan Speed:

- Total Distance (D): 500 cm
- Elapsed Time (T): 5.6 seconds

[tex]\[ \text{Average Velocity} = \frac{500 \text{ cm}}{5.6 \text{ s}} \approx 89.3 \text{ cm/s} \][/tex]

So, the average velocities, rounded to the nearest tenth, are:

- The cart with Low fan speed has an average velocity of \( 67.6 \) cm/s.
- The cart with Medium fan speed has an average velocity of \( 78.1 \) cm/s.
- The cart with High fan speed has an average velocity of [tex]\( 89.3 \)[/tex] cm/s.