Certainly! Let's go through each part of the problem:
### a. Plotting the Graph
First, let's plot the provided data points to visualize the speed of the object over time.
The given data points are:
- Time (s): [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]
- Speed (m/s): [3.0, 6.1, 8.8, 12.0, 15.3, 17.9]
To create the graph, you would use graphing technology of your choice (such as graphing software, or even manually on graph paper).
The resulting graph should show a trend indicating that as time increases, the speed increases as well. You could apply a curve fit line or a linear fit, depending on the pattern. In this case, we'll assume we used a linear fit for simplicity.
### b. Interpolation
Interpolation involves finding a value within the range of the given data points. For instance, if you want to find the speed of the object at a time of 3.5 seconds (which falls within the given range of 1.0 to 6.0 seconds):
- Given Time (s): 3.5
We look for the corresponding speed value at this time within the given data range. The interpolated speed at 3.5 seconds is:
- Interpolated Speed (m/s): 10.4
### c. Extrapolation
Extrapolation involves predicting a value outside the range of the given data points. For example, if you want to estimate the speed of the object at a future time of 7.0 seconds (which is outside the given range of 1.0 to 6.0 seconds):
- Given Time (s): 7.0
We use the trend of the data to predict the speed beyond the last recorded time. The extrapolated speed at 7.0 seconds is:
- Extrapolated Speed (m/s): 21.04
### Summary:
- b. The interpolated value on the graph for the time 3.5 seconds is 10.4 m/s.
- c. The extrapolated value on the graph for the time 7.0 seconds is 21.04 m/s.
Make sure to attach the graph image with your name and the current date, showing the interpolation point at 3.5 seconds and the extrapolation point at 7.0 seconds, indicating their corresponding speed values.
