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:

Assuming the problem is to find the speed of the cheetah (since it's a distance - time graph, speed = distance / time):

Step1: Identify two points on the graph

We can take the points \((0,0)\) and \((8,200)\) (or any other two points like \((2,50)\), \((4,100)\), \((6,150)\)). Let's use \((0,0)\) and \((8,200)\). The formula for speed \(v\) is \(v=\frac{\text{change in distance}}{\text{change in time}}\).

Step2: Calculate the change in distance and time

The change in distance \(\Delta d=200 - 0=200\) meters. The change in time \(\Delta t = 8-0 = 8\) seconds.

Step3: Calculate the speed

Using the formula \(v=\frac{\Delta d}{\Delta t}\), we substitute \(\Delta d = 200\) m and \(\Delta t=8\) s. So \(v=\frac{200}{8}=25\) m/s. We can also check with other points, for example, using \((2,50)\): \(\frac{50 - 0}{2-0}=\frac{50}{2} = 25\) m/s, which confirms the speed.

Answer:

The speed of the cheetah is \(25\) meters per second.