To determine the order of accelerations from least to most for Max, Finley, and Xander, we need to calculate the acceleration for each individual. Since they all start from rest, the acceleration [tex]\(a\)[/tex] can be found using the formula:
[tex]\[ a = \frac{v}{t} \][/tex]
where [tex]\( v \)[/tex] is the final velocity and [tex]\( t \)[/tex] is the time taken to reach that velocity.
Step-by-Step Solution:
1. Calculate Max's acceleration:
- Final velocity, [tex]\( v_{Max} = 7.3 \, \text{m/s} \)[/tex]
- Time taken, [tex]\( t_{Max} = 1.2 \, \text{s} \)[/tex]
[tex]\[ a_{Max} = \frac{v_{Max}}{t_{Max}} = \frac{7.3}{1.2} \][/tex]
[tex]\[ a_{Max} \approx 6.083 \, \text{m/s}^2 \][/tex]
2. Calculate Finley's acceleration:
- Final velocity, [tex]\( v_{Finley} = 3.6 \, \text{m/s} \)[/tex]
- Time taken, [tex]\( t_{Finley} = 4.2 \, \text{s} \)[/tex]
[tex]\[ a_{Finley} = \frac{v_{Finley}}{t_{Finley}} = \frac{3.6}{4.2} \][/tex]
[tex]\[ a_{Finley} \approx 0.857 \, \text{m/s}^2 \][/tex]
3. Calculate Xander's acceleration:
- Final velocity, [tex]\( v_{Xander} = 4.5 \, \text{m/s} \)[/tex]
- Time taken, [tex]\( t_{Xander} = 3.5 \, \text{s} \)[/tex]
[tex]\[ a_{Xander} = \frac{v_{Xander}}{t_{Xander}} = \frac{4.5}{3.5} \][/tex]
[tex]\[ a_{Xander} \approx 1.286 \, \text{m/s}^2 \][/tex]
Now, we compare the calculated accelerations:
- [tex]\( a_{Finley} \approx 0.857 \, \text{m/s}^2 \)[/tex]
- [tex]\( a_{Xander} \approx 1.286 \, \text{m/s}^2 \)[/tex]
- [tex]\( a_{Max} \approx 6.083 \, \text{m/s}^2 \)[/tex]
When we list them from least to most acceleration, we get:
1. Finley
2. Xander
3. Max
Therefore, the correct order from least to most acceleration is:
Finley → Xander → Max
