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The chart shows the times and accelerations for three drivers.

\begin{tabular}{|l|l|l|}
\hline Driver & Acceleration & Time \\
\hline Kira & [tex]$5.2 \, m/s^2$[/tex] & 6.9 sec \\
\hline Dustin & [tex]$8.3 \, m/s^2$[/tex] & 3 sec \\
\hline Diego & [tex]$6.5 \, m/s^2$[/tex] & 4.2 sec \\
\hline
\end{tabular}

Which lists them from greatest to lowest change in velocity?

A. Dustin [tex]$\rightarrow$[/tex] Diego [tex]$\rightarrow$[/tex] Kira

B. Dustin [tex]$\rightarrow$[/tex] Kira [tex]$\rightarrow$[/tex] Diego

C. Kira [tex]$\rightarrow$[/tex] Dustin [tex]$\rightarrow$[/tex] Diego

D. Kira [tex]$\rightarrow$[/tex] Diego [tex]$\rightarrow$[/tex] Dustin


Sagot :

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