To determine which driver experienced the greatest to lowest change in velocity, we need to calculate the change in velocity for each driver. The formula for change in velocity is:
[tex]\[ \Delta v = a \times t \][/tex]
where [tex]\( \Delta v \)[/tex] is the change in velocity, [tex]\( a \)[/tex] is the acceleration, and [tex]\( t \)[/tex] is the time.
Let's calculate the change in velocity for each driver step-by-step:
### Kira
- Acceleration ([tex]\( a \)[/tex]): [tex]\( 5.2 \, \text{m/s}^2 \)[/tex]
- Time ([tex]\( t \)[/tex]): [tex]\( 6.9 \, \text{seconds} \)[/tex]
[tex]\[ \Delta v_{\text{Kira}} = 5.2 \, \text{m/s}^2 \times 6.9 \, \text{seconds} = 35.88 \, \text{m/s} \][/tex]
### Dustin
- Acceleration ([tex]\( a \)[/tex]): [tex]\( 8.3 \, \text{m/s}^2 \)[/tex]
- Time ([tex]\( t \)[/tex]): [tex]\( 3 \, \text{seconds} \)[/tex]
[tex]\[ \Delta v_{\text{Dustin}} = 8.3 \, \text{m/s}^2 \times 3 \, \text{seconds} = 24.9 \, \text{m/s} \][/tex]
### Diego
- Acceleration ([tex]\( a \)[/tex]): [tex]\( 6.5 \, \text{m/s}^2 \)[/tex]
- Time ([tex]\( t \)[/tex]): [tex]\( 4.2 \, \text{seconds} \)[/tex]
[tex]\[ \Delta v_{\text{Diego}} = 6.5 \, \text{m/s}^2 \times 4.2 \, \text{seconds} = 27.3 \, \text{m/s} \][/tex]
Now that we have the change in velocity for each driver, we can list them from greatest to lowest:
1. Kira: [tex]\( 35.88 \, \text{m/s} \)[/tex]
2. Diego: [tex]\( 27.3 \, \text{m/s} \)[/tex]
3. Dustin: [tex]\( 24.9 \, \text{m/s} \)[/tex]
Therefore, the correct order from greatest to lowest change in velocity is:
Kira [tex]\( \rightarrow \)[/tex] Diego [tex]\( \rightarrow \)[/tex] Dustin
So, the correct answer is:
Kira [tex]\( \rightarrow \)[/tex] Diego [tex]\( \rightarrow \)[/tex] Dustin
