Question

the chart shows the times and accelerations for three drivers. which lists them from greatest to lowest change in velocity? dustin → diego → kira dustin → kira → diego kira → dustin → diego kira → diego → dustin

Explanation:

Step1: Recall the formula for change in velocity

The change in velocity ($\Delta v$) is given by the product of acceleration ($a$) and time ($t$), so $\Delta v = a \times t$.

Step2: Calculate $\Delta v$ for Kira

Kira's acceleration $a = 5.2\ m/s^2$ and time $t = 6.9\ sec$. So, $\Delta v_{Kira} = 5.2 \times 6.9 = 35.88\ m/s$.

Step3: Calculate $\Delta v$ for Dustin

Dustin's acceleration $a = 8.3\ m/s^2$ and time $t = 3\ sec$. So, $\Delta v_{Dustin} = 8.3 \times 3 = 24.9\ m/s$. Wait, no, wait, let's recalculate. Wait, 8.33 is 24.9? Wait, no, wait, maybe I made a mistake. Wait, no, let's check again. Wait, Kira: 5.26.9. 56.9=34.5, 0.26.9=1.38, so total 35.88. Dustin: 8.33=24.9? Wait, no, that can't be. Wait, no, maybe I mixed up. Wait, Diego: 6.54.2. 64.2=25.2, 0.54.2=2.1, so 27.3. Oh! Wait, I see my mistake. I miscalculated Dustin and Diego. Let's redo:

Step2 (corrected): Calculate $\Delta v$ for Kira

$\Delta v_{Kira} = 5.2 \times 6.9$. Let's compute: 5.26 = 31.2, 5.20.9=4.68, so 31.2+4.68=35.88 m/s.

Step3 (corrected): Calculate $\Delta v$ for Dustin

$\Delta v_{Dustin} = 8.3 \times 3 = 24.9$? Wait, no, 83=24, 0.33=0.9, so 24.9. Wait, but Diego: 6.54.2. 64.2=25.2, 0.5*4.2=2.1, so 25.2+2.1=27.3 m/s.

Wait, so now: Kira: 35.88, Diego:27.3, Dustin:24.9? Wait, that would mean Kira has the highest, then Diego, then Dustin. But that contradicts the options. Wait, no, wait, the options are Dustin → Diego → Kira; Dustin → Kira → Diego; Kira → Dustin → Diego; Kira → Diego → Dustin. Wait, so my calculations must be wrong. Wait, let's check the formula again. The change in velocity is acceleration multiplied by time, because $a = \frac{\Delta v}{\Delta t}$, so $\Delta v = a \times \Delta t$. So that's correct. So let's recalculate all three:

• Kira: $a = 5.2\ m/s^2$, $t = 6.9\ s$. $\Delta v = 5.2 \times 6.9$. Let's compute 5.2*6.9:

5.2 * 6.9:
= (5 + 0.2) * 6.9
= 56.9 + 0.26.9
= 34.5 + 1.38
= 35.88 m/s.

• Dustin: $a = 8.3\ m/s^2$, $t = 3\ s$. $\Delta v = 8.3 \times 3 = 24.9\ m/s$.

• Diego: $a = 6.5\ m/s^2$, $t = 4.2\ s$. $\Delta v = 6.5 \times 4.2$. Let's compute:

6.5 * 4.2:
= (6 + 0.5) * 4.2
= 64.2 + 0.54.2
= 25.2 + 2.1
= 27.3\ m/s.

Now, let's list the $\Delta v$ values:

• Kira: 35.88

• Diego: 27.3

• Dustin: 24.9

So from greatest to lowest: Kira (35.88) → Diego (27.3) → Dustin (24.9). Wait, but the options are:

1. Dustin → Diego → Kira

1. Dustin → Kira → Diego

1. Kira → Dustin → Diego

1. Kira → Diego → Dustin

Wait, according to our calculations, Kira (35.88) is highest, then Diego (27.3), then Dustin (24.9). So that's Kira → Diego → Dustin, which is option 4. But wait, did I miscalculate Dustin? Wait, 8.33: 83=24, 0.33=0.9, so 24.9. Correct. Diego: 6.54.2=27.3. Correct. Kira: 5.2*6.9=35.88. Correct. So the order is Kira (35.88) > Diego (27.3) > Dustin (24.9). So the option is Kira → Diego → Dustin, which is the fourth option. Wait, but let's check the options again. The options are:

• Dustin → Diego → Kira

• Dustin → Kira → Diego

• Kira → Dustin → Diego

• Kira → Diego → Dustin

Yes, the fourth option is Kira → Diego → Dustin, which matches our calculation. Wait, but initially, I thought I made a mistake, but after recalculating, that's correct. So the correct order is Kira (35.88) > Diego (27.3) > Dustin (24.9), so the list from greatest to lowest is Kira → Diego → Dustin.

Answer:

Kira → Diego → Dustin (the fourth option, i.e., the option with "Kira → Diego → Dustin")