Question

a wildlife biologist is studying wild cheetahs. she takes a video of a cheetah running at its top speed. then, she uses the video to make the graph of the cheetah’s distance vs. time shown below:

Explanation:

Since the problem is not fully stated (e.g., what is being asked about the graph, like finding speed, interpreting the graph, etc.), we can't provide a complete solution. But if we assume the common question is to find the speed (which is the slope of the distance - time graph), here is how we would solve it:

Step1: Recall the formula for speed

Speed $v$ is calculated as the ratio of distance $d$ to time $t$, i.e., $v=\frac{d}{t}$. From the distance - time graph, we can pick two points. Let's take the points $(0,0)$ and $(8,200)$ (or any other two points on the line, like $(2,50)$, $(4,100)$, $(6,150)$ which will give the same result).

Step2: Calculate the speed

Using the points $(t_1,d_1)=(0,0)$ and $(t_2,d_2)=(8,200)$, the speed $v = \frac{d_2 - d_1}{t_2 - t_1}=\frac{200 - 0}{8 - 0}=\frac{200}{8}=25$ m/s. If we use the point $(2,50)$, then $v=\frac{50 - 0}{2 - 0}=\frac{50}{2} = 25$ m/s, which is the same.

If the actual question was different (e.g., interpreting the graph, finding distance at a certain time, etc.), the steps would change accordingly. Since the question is not fully provided, we can only give a general approach based on common problems related to distance - time graphs.

If you want to find the speed of the cheetah:

Step1: Identify two points on the graph

We can use the points $(0,0)$ (when time $t = 0$ seconds, distance $d=0$ meters) and $(8,200)$ (when time $t = 8$ seconds, distance $d = 200$ meters).

Step2: Use the speed formula

The formula for speed $v$ is $v=\frac{\text{change in distance}}{\text{change in time}}=\frac{d_2 - d_1}{t_2 - t_1}$. Substituting $d_1 = 0$, $t_1=0$, $d_2 = 200$, $t_2 = 8$ into the formula, we get $v=\frac{200 - 0}{8 - 0}=\frac{200}{8}=25$.

Answer:

The speed of the cheetah is 25 meters per second.