Build a table showing the character's position starting from 0.0 centimeters and pressing the button for 0.6 seconds. How would you calculate the unit rate for the character’s new motion? Create a graph showing the character's position in centimeters versus the time in seconds. You can draw it by hand or use a spreadsheet program if you know how to. Write an equation to describe how the character's position depends on time. Measure the width of your computer screen and predict how long it would take the character to move across the screen starting from the left edge
To build the table, we will assume a constant velocity of the character when the button is pressed for 0.6 seconds.
Time (s) | Position (cm)
------------ | -------------
0.0 | 0.0
0.6 | X
To calculate the unit rate for the character's new motion, we need to determine the change in position per unit of time.
Unit rate = Change in position / Change in time
Since the character starts from 0.0 cm and moves to an unknown position (denoted as X) in 0.6 seconds, the change in position is X - 0.0 = X cm and the change in time is 0.6 - 0.0 = 0.6 seconds.
Unit rate = (X - 0.0) cm / (0.6 - 0.0) s = X cm/s
To create a graph showing the character's position in centimeters versus time in seconds, follow these steps:
1. Label the x-axis as "Time (s)" and the y-axis as "Position (cm)."
2. Plot the points (0.0, 0.0) and (0.6, X) on the graph.
3. Draw a straight line connecting these two points.
The equation to describe how the character's position depends on time can be found using the slope-intercept form of a linear equation:
y = mx + b
In this case, y represents the position (cm) and x represents the time (s). The slope (m) is the unit rate we calculated earlier, which is X cm/s. The intercept (b) represents the starting position, which is 0.0 cm.
Therefore, the equation can be written as:
Position (cm) = X (cm/s) * Time (s) + 0.0
Since the width of computer screens can vary, we cannot provide an accurate prediction of how long it would take for the character to move across the screen starting from the left edge without knowing the screen width in centimeters.
To build the table, we can use the formula for constant acceleration:
$$
\text{position} = \text{initial position} + (\text{initial velocity}\times \text{time}) + (0.5\times \text{acceleration}\times \text{time}^2)
$$
Given that the initial position is 0.0 cm, the initial velocity is 0 cm/s (since the character starts from rest), and the acceleration is 0.6 cm/s², we can calculate the position for different times.
Let's calculate the position at regular intervals of time:
Time(seconds) | Position(cm)
-------------------------------
0.0 | 0.0
0.1 | 0.003
0.2 | 0.012
0.3 | 0.027
0.4 | 0.048
0.5 | 0.075
0.6 | 0.108
To calculate the unit rate for the character's new motion, we can use the formula:
$$
\text{unit rate} = \frac{\text{change in position}}{\text{change in time}}
$$
In this case, the change in position over 0.6 seconds is 0.108 cm - 0 cm = 0.108 cm, and the change in time is 0.6 s - 0 s = 0.6 s. Therefore, the unit rate for the character's new motion is:
$$
\text{unit rate} = \frac{0.108 \text{ cm}}{0.6 \text{ s}} \approx 0.18 \text{ cm/s}
$$
To create the graph showing the character's position in centimeters versus time in seconds, we can use a spreadsheet program like Microsoft Excel or Google Sheets. We can plot the time values on the x-axis and the position values on the y-axis.
Here is a hand-drawn representation of the graph:
```
Position (cm)
|
| .
| .
| .
| .
| .
---------------------------------------------------
Time (s) 0.6
```
The equation to describe how the character's position depends on time is:
$$
\text{position} = 0.5 \times 0.6 \times t^2
$$
Where t represents time in seconds.
To measure the width of your computer screen and predict how long it would take the character to move across the screen starting from the left edge, you need to measure the width of your screen in centimeters. Let's say the width of your computer screen is 40 cm.
Using the equation for position:
$$
\text{position} = 0.5 \times 0.6 \times t^2
$$
We can rearrange the equation to solve for time:
$$
t = \sqrt{\frac{2 \times \text{position}}{0.6}}
$$
Substituting the position as the width of the screen (40 cm), we get:
$$
t = \sqrt{\frac{2 \times 40}{0.6}}
$$
Calculating the value, we find:
$$
t \approx 10.95 \text{ seconds}
$$
So, it would take approximately 10.95 seconds for the character to move across the screen starting from the left edge.
To answer these questions and complete the tasks, follow these steps:
Step 1: Build a table showing the character's position:
- Use the formula: position = initial position + (speed × time)
- Assuming the character starts at 0.0 centimeters and travels at a constant speed, we need to determine the speed. The speed can be calculated using the formula: speed = distance / time.
- Given the button press duration is 0.6 seconds, the distance traveled will depend on the speed of the character.
Step 2: Calculate the unit rate for the character's motion:
- Unit rate represents the amount of change in position per unit of time. In this case, it will be the rate at which the character moves in centimeters per second.
- To calculate the unit rate, divide the change in position (in centimeters) by the change in time (in seconds).
Step 3: Create a graph showing the character's position versus time:
- Use a spreadsheet program like Microsoft Excel or Google Sheets to create a table with columns for time and position.
- Plot the time values on the x-axis and the corresponding position values on the y-axis to create a line graph.
Step 4: Write an equation to describe the character's position:
- From the table or graph, observe the relationship between the character's position and time.
- Based on the given information, the equation for the character's position will likely be a linear equation of the form: position = initial position + (speed × time).
Step 5: Measure the width of your computer screen and predict the time to move across:
- Use a ruler or measuring tape to measure the width of your computer screen in centimeters.
- Based on the character's speed and the equation developed earlier, substitute the width of the screen for the position in the equation.
- Solve the equation to find the time it would take for the character to move across the screen.
By following these steps, you will be able to calculate the unit rate, create a graph showing the character's position, write an equation describing the position, and predict the time it would take for the character to move across your computer screen.