Answered

Get the information you need from a community of experts on IDNLearn.com. Ask your questions and receive reliable and comprehensive answers from our dedicated community of professionals.

The chart shows data for an object moving at a constant acceleration.

| Time (s) | Velocity (m/s) |
|----------|-----------------|
| 0 | 0 |
| 1 | X |
| 2 | Y |
| 3 | Z |

Which values best complete the chart?

A. X: 0, Y: 0, Z: 1
B. X: 2, Y: 4, Z: 6
C. X: 3, Y: 3, Z: 3
D. X: 1, Y: 5, Z: 8

Sagot :

GinnyAnsweridn
Let's analyze the problem to find the values for [tex]\(X\)[/tex], [tex]\(Y\)[/tex], and [tex]\(Z\)[/tex] that best complete the chart of the object's velocity over time considering constant acceleration.

We're given four options for [tex]\(X\)[/tex], [tex]\(Y\)[/tex], and [tex]\(Z\)[/tex]:
1. [tex]\(X = 0\)[/tex], [tex]\(Y = 0\)[/tex], [tex]\(Z = 1\)[/tex]
2. [tex]\(X = 2\)[/tex], [tex]\(Y = 4\)[/tex], [tex]\(Z = 6\)[/tex]
3. [tex]\(X = 3\)[/tex], [tex]\(Y = 3\)[/tex], [tex]\(Z = 3\)[/tex]
4. [tex]\(X = 1\)[/tex], [tex]\(Y = 5\)[/tex], [tex]\(Z = 8\)[/tex]

Since the object is moving with constant acceleration, its velocity should follow a linear pattern, where the change in velocity is the same over equal intervals of time.

Let's evaluate each option:

1. [tex]\(X = 0\)[/tex], [tex]\(Y = 0\)[/tex], [tex]\(Z = 1\)[/tex]
- From [tex]\(t = 0\)[/tex] to [tex]\(t = 1\)[/tex]: Velocity changes from 0 to 0.
- From [tex]\(t = 1\)[/tex] to [tex]\(t = 2\)[/tex]: Velocity changes from 0 to 0.
- From [tex]\(t = 2\)[/tex] to [tex]\(t = 3\)[/tex]: Velocity changes from 0 to 1.
This does not indicate a constant acceleration.

2. [tex]\(X = 2\)[/tex], [tex]\(Y = 4\)[/tex], [tex]\(Z = 6\)[/tex]
- From [tex]\(t = 0\)[/tex] to [tex]\(t = 1\)[/tex]: Velocity changes from 0 to 2.
- From [tex]\(t = 1\)[/tex] to [tex]\(t = 2\)[/tex]: Velocity changes from 2 to 4.
- From [tex]\(t = 2\)[/tex] to [tex]\(t = 3\)[/tex]: Velocity changes from 4 to 6.
This shows a constant acceleration with equal changes (+2) in velocity over each time interval.

3. [tex]\(X = 3\)[/tex], [tex]\(Y = 3\)[/tex], [tex]\(Z = 3\)[/tex]
- From [tex]\(t = 0\)[/tex] to [tex]\(t = 1\)[/tex]: Velocity changes from 0 to 3.
- From [tex]\(t = 1\)[/tex] to [tex]\(t = 2\)[/tex]: Velocity remains 3.
- From [tex]\(t = 2\)[/tex] to [tex]\(t = 3\)[/tex]: Velocity remains 3.
This does not show a constant acceleration; rather, it shows constant velocity from [tex]\(t = 1\)[/tex] onwards.

4. [tex]\(X = 1\)[/tex], [tex]\(Y = 5\)[/tex], [tex]\(Z = 8\)[/tex]
- From [tex]\(t = 0\)[/tex] to [tex]\(t = 1\)[/tex]: Velocity changes from 0 to 1.
- From [tex]\(t = 1\)[/tex] to [tex]\(t = 2\)[/tex]: Velocity changes from 1 to 5.
- From [tex]\(t = 2\)[/tex] to [tex]\(t = 3\)[/tex]: Velocity changes from 5 to 8.
This shows a non-linear increase in velocity, indicating inconsistent acceleration.

The values that best complete the chart for an object moving at a constant acceleration are:
[tex]\[X = 2, Y = 4, Z = 6\][/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.