Let’s break down the questions based on the graph and the problem you're looking to solve.

Part (a): Calculate the average speed between 2 and 8 seconds.

The average speed is given by the formula:

$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$

From the graph, you can find the distance at 2 seconds and 8 seconds.

• Distance at 2 seconds: about 8 meters.
• Distance at 8 seconds: about 70 meters.

Thus, the total distance is:

$70 \, \text{m} - 8 \, \text{m} = 62 \, \text{m}$

The total time is:

$8 \, \text{seconds} - 2 \, \text{seconds} = 6 \, \text{seconds}$

So, the average speed is:

$\text{Average speed} = \frac{62 \, \text{m}}{6 \, \text{seconds}} = 10.33 \, \text{m/s}$

Part (b): Estimate the speed of the animal at 6 seconds.

To estimate the speed at a specific point, we need to find the slope of the curve at 6 seconds. This is equivalent to the instantaneous rate of change or the derivative at that point, which can be approximated by drawing a tangent line to the curve at 6 seconds.

Looking at the graph, the slope at 6 seconds appears to be steep. From a rough estimate of the graph, the speed at 6 seconds is approximately:

$\text{Speed at 6 seconds} \approx 20 \, \text{m/s}$

Part (c): Does the animal move faster than 20 m/s?

From part (b), we estimated the speed at 6 seconds to be about 20 m/s. However, since the graph shows the speed increases very steeply after 6 seconds, it's clear that the animal is accelerating.

To determine if Nuri’s claim that the animal can move over 20 m/s is reasonable, we can observe that the graph indicates the speed at later points (for example, at 10 seconds) could exceed 20 m/s, meaning Nuri’s statement is likely true.

Let me know if you would like to dive deeper into any part of this analysis, or if you have further questions! Here are some additional related questions to explore:

1. How do you calculate the instantaneous speed at a given point?
2. What does the steepness of a graph tell us about the animal's acceleration?
3. What are the units for speed and how do they relate to the graph?
4. How do you calculate the area under the curve, and what does it represent in this context?
5. What is the difference between average speed and instantaneous speed?

Tip: When estimating the speed from a graph, the key is identifying the slope of the tangent line at the point of interest.