Question

d) the cheetah traveled 1.75 times faster for the first 8 minutes than it did for the second 8 minutes. was the distance traveled during the first 8 minutes 1.75 times greater than the distance traveled during the second 8 minutes? show the calculation to justify your answer

Explanation:

Step1: Recall the distance - speed - time formula

The formula for distance is $d = vt$, where $d$ is distance, $v$ is speed, and $t$ is time.
Let the speed of the cheetah in the second 8 - minute period be $v_2$, and the speed in the first 8 - minute period be $v_1$. We know that $v_1=1.75v_2$.
The time for both periods is $t_1 = t_2=8$ minutes.

Step2: Calculate the distances for each period

The distance traveled in the first 8 - minute period, $d_1=v_1t_1$. Since $v_1 = 1.75v_2$ and $t_1 = 8$, we have $d_1=1.75v_2\times8$.
The distance traveled in the second 8 - minute period, $d_2=v_2t_2$. Since $t_2 = 8$, we have $d_2=v_2\times8$.

Step3: Find the ratio of the two distances

$\frac{d_1}{d_2}=\frac{1.75v_2\times8}{v_2\times8}$. The $v_2$ and 8 terms cancel out, and we get $\frac{d_1}{d_2}=1.75$.

Answer:

Yes, the distance traveled during the first 8 minutes was 1.75 times greater than the distance traveled during the second 8 minutes.