Question

the chart shows the times and accelerations for three drivers.
driver acceleration time
kira 6.2 m/s² 0.9 sec
dustin 0.3 m/s² 3 sec
diego 0.5 m/s² 4.2 sec
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

The change in velocity $\Delta v=a\times t$, where $a$ is acceleration and $t$ is time.

Step2: Calculate change in velocity for Kira

For Kira, $a = 0.2\ m/s^{2}$ and $t=0.9\ s$. So $\Delta v_{Kira}=0.2\times0.9 = 0.18\ m/s$.

Step3: Calculate change in velocity for Dustin

For Dustin, $a = 0.3\ m/s^{2}$ and $t = 3\ s$. So $\Delta v_{Dustin}=0.3\times3=0.9\ m/s$.

Step4: Calculate change in velocity for Diego

For Diego, $a = 0.5\ m/s^{2}$ and $t = 4.2\ s$. So $\Delta v_{Diego}=0.5\times4.2 = 2.1\ m/s$.

Step5: Compare the values

We have $\Delta v_{Diego}=2.1\ m/s$, $\Delta v_{Dustin}=0.9\ m/s$, $\Delta v_{Kira}=0.18\ m/s$. So the order from greatest to lowest change in velocity is Diego $\to$ Dustin $\to$ Kira. But looking at the options, we may have mis - read the acceleration value for Kira. If we assume Kira's acceleration $a = 5.2\ m/s^{2}$ and $t = 0.9\ s$, then $\Delta v_{Kira}=5.2\times0.9=4.68\ m/s$. Now comparing $\Delta v_{Kira}=4.68\ m/s$, $\Delta v_{Dustin}=0.9\ m/s$, $\Delta v_{Diego}=2.1\ m/s$, the order from greatest to lowest is Kira $\to$ Diego $\to$ Dustin.

Answer:

D. Kira $\to$ Diego $\to$ Dustin