To determine the order of drivers based on their change in velocity from greatest to lowest, we need to calculate the change in velocity ([tex]\( \Delta v \)[/tex]) for each driver. The change in velocity is given by the formula:
[tex]\[ \Delta v = a \times t \][/tex]
where [tex]\( a \)[/tex] is the acceleration and [tex]\( t \)[/tex] is the time.
Let's calculate [tex]\( \Delta v \)[/tex] for each driver:
1. Kira:
- Acceleration: [tex]\( 5.2 \, m/s^2 \)[/tex]
- Time: [tex]\( 6.9 \, s \)[/tex]
- Change in velocity: [tex]\( \Delta v_{\text{Kira}} = 5.2 \times 6.9 = 35.88 \, m/s \)[/tex]
2. Dustin:
- Acceleration: [tex]\( 8.3 \, m/s^2 \)[/tex]
- Time: [tex]\( 3 \, s \)[/tex]
- Change in velocity: [tex]\( \Delta v_{\text{Dustin}} = 8.3 \times 3 = 24.9 \, m/s \)[/tex]
3. Diego:
- Acceleration: [tex]\( 6.5 \, m/s^2 \)[/tex]
- Time: [tex]\( 4.2 \, s \)[/tex]
- Change in velocity: [tex]\( \Delta v_{\text{Diego}} = 6.5 \times 4.2 = 27.3 \, m/s \)[/tex]
Now, we list the changes in velocity in descending order:
- Kira: [tex]\( 35.88 \, m/s \)[/tex]
- Diego: [tex]\( 27.3 \, m/s \)[/tex]
- Dustin: [tex]\( 24.9 \, m/s \)[/tex]
So, the order from greatest to lowest change in velocity is:
Kira → Diego → Dustin
Hence, the correct listing from greatest to lowest change in velocity is:
[tex]\[ \text{Kira} \rightarrow \text{Diego} \rightarrow \text{Dustin} \][/tex]
