To determine the correct values for [tex]\(X\)[/tex], [tex]\(Y\)[/tex], and [tex]\(Z\)[/tex] that complete the chart of an object moving at a constant acceleration, we need to consider the given options and the nature of uniformly accelerated motion.
Let's analyze each option given:
1. Option 1:
- [tex]\(X: 0\)[/tex]
- [tex]\(Y: 0\)[/tex]
- [tex]\(Z: 1\)[/tex]
This option suggests that the velocity does not change from [tex]\(t = 0\)[/tex] to [tex]\(t = 2\)[/tex] seconds and then suddenly increases at [tex]\(t = 3\)[/tex] seconds, which does not align with the concept of constant acceleration. Therefore, this option is incorrect.
2. Option 2:
- [tex]\(X: 2\)[/tex]
- [tex]\(Y: 4\)[/tex]
- [tex]\(Z: 6\)[/tex]
This set of values shows a linear increase in velocity, which is characteristic of constant acceleration. The velocity increases by [tex]\(2\)[/tex] m/s every second, indicating a constant acceleration. Therefore, this set of values could be correct.
3. Option 3:
- [tex]\(X: 3\)[/tex]
- [tex]\(Y: 3\)[/tex]
- [tex]\(Z: 3\)[/tex]
This option suggests the velocity is constant and does not change over time, which contradicts the premise of constant acceleration. Thus, this option is incorrect.
4. Option 4:
- [tex]\(X: 1\)[/tex]
- [tex]\(Y: 5\)[/tex]
- [tex]\(Z: 8\)[/tex]
This set of values does not show a linear increase in velocity, as the difference between successive values ([tex]\(X\)[/tex] to [tex]\(Y\)[/tex] and [tex]\(Y\)[/tex] to [tex]\(Z\)[/tex]) is not consistent. Hence, this does not align with constant acceleration and is incorrect.
Considering the characteristics of constant acceleration and the provided answer options, the correct values are:
- [tex]\(X: 2\)[/tex]
- [tex]\(Y: 4\)[/tex]
- [tex]\(Z: 6\)[/tex]
Thus, the values that best complete the chart are:
- [tex]\(X = 2\)[/tex]
- [tex]\(Y = 4\)[/tex]
- [tex]\(Z = 6\)[/tex]
