To determine the speeds of both Object A and Object B, we can analyze the data provided for Object A and the equation for Object B.
Object A:
We have the following data points for Object A:
| x | y | |---|---| | 4 | 1 | | 8 | 2 | | 12 | 3 | | 16 | 4 |
The relationship between x and y shows a linear pattern. We can find the speed (or rate of change) by looking at the change in y values over the change in x values:
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From (4, 1) to (8, 2):
- Δy = 2 - 1 = 1
- Δx = 8 - 4 = 4
- Speed = Δy / Δx = 1 / 4 = 0.25
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From (8, 2) to (12, 3):
- Δy = 3 - 2 = 1
- Δx = 12 - 8 = 4
- Speed = 1 / 4 = 0.25
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From (12, 3) to (16, 4):
- Δy = 4 - 3 = 1
- Δx = 16 - 12 = 4
- Speed = 1 / 4 = 0.25
The speed for Object A is consistently 0.25.
Object B:
The equation given for Object B is: \[ y = \frac{1}{5} x \]
To find the speed of Object B, we can deduce it from the slope of the equation:
- The equation shows that for every increase of 5 in x, y increases by 1.
- Thus, the speed (rate of change of y with respect to x) is \( \frac{1}{5} = 0.2 \).
Comparison of Speeds:
- Speed of Object A = 0.25
- Speed of Object B = 0.2
Now, we can compare the two speeds:
- Since 0.25 is greater than 0.2, Object A is faster.
To find the factor by which Object A is faster than Object B: \[ \text{Factor} = \frac{\text{Speed of Object A}}{\text{Speed of Object B}} = \frac{0.25}{0.2} = 1.25 \]
Conclusion:
The faster object is Object A compared to Object B, and the factor by which Object A is faster is 1.25.
Thus, the correct option is: C: Object A is moving faster by a factor of 1.25.
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