To calculate the average velocity of the cart for each fan speed, we can use the formula for average velocity, which is:
[tex]\[ \text{Average Velocity} = \frac{\text{Total Distance}}{\text{Elapsed Time}} \][/tex]
Given:
- Total distance to the finish line: [tex]\( 500 \ \text{cm} \)[/tex]
- Elapsed time for Low fan speed: [tex]\( 7.4 \ \text{s} \)[/tex]
- Elapsed time for Medium fan speed: [tex]\( 6.4 \ \text{s} \)[/tex]
- Elapsed time for High fan speed: [tex]\( 5.6 \ \text{s} \)[/tex]
### Step-by-Step Calculation:
1. Calculate the average velocity for Low fan speed:
[tex]\[ \text{Average Velocity}_{\text{Low}} = \frac{500 \ \text{cm}}{7.4 \ \text{s}} = 67.6 \ \text{cm/s} \][/tex]
2. Calculate the average velocity for Medium fan speed:
[tex]\[ \text{Average Velocity}_{\text{Medium}} = \frac{500 \ \text{cm}}{6.4 \ \text{s}} = 78.1 \ \text{cm/s} \][/tex]
3. Calculate the average velocity for High fan speed:
[tex]\[ \text{Average Velocity}_{\text{High}} = \frac{500 \ \text{cm}}{5.6 \ \text{s}} = 89.3 \ \text{cm/s} \][/tex]
### Final Results:
- The cart with Low fan speed has an average velocity of [tex]\( 67.6 \ \text{cm/s} \)[/tex].
- The cart with Medium fan speed has an average velocity of [tex]\( 78.1 \ \text{cm/s} \)[/tex].
- The cart with High fan speed has an average velocity of [tex]\( 89.3 \ \text{cm/s} \)[/tex].
