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.
