Which set of graphs illustrates identical motion patterns for an object?

Question

(1 point)
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In the Position versus Time graph, the horizontal axis is Time and the vertical axis is Position. The line begins at the top of the vertical axis and has a negative, linear slope. In the Velocity versus Time graph, the horizontal axis is Time and the vertical axis is Velocity. The line begins at the origin and has a positive, linear slope.
Image with alt text: In the Position versus Time graph, the horizontal axis is Time and the vertical axis is Position. The line begins at the top of the vertical axis and has a negative, linear slope. In the Velocity versus Time graph, the horizontal axis is Time and the vertical axis is Velocity. The line begins at the origin and has a positive, linear slope.

In the Position versus Time graph, the horizontal axis is Time and the vertical axis is Position. The line begins at the origin and has a positive, linear slope. In the Velocity versus Time graph, the horizontal axis is Time and the vertical axis is Velocity. The line begins at the origin and has a positive, linear slope.
Image with alt text: In the Position versus Time graph, the horizontal axis is Time and the vertical axis is Position. The line begins at the origin and has a positive, linear slope. In the Velocity versus Time graph, the horizontal axis is Time and the vertical axis is Velocity. The line begins at the origin and has a positive, linear slope.

In the Position versus Time graph, the horizontal axis is Time and the vertical axis is Position. The line begins at the origin and has a positive, linear slope. In the Velocity versus Time graph, the horizontal axis is Time and the vertical axis is Velocity. The line begins from the middle of the vertical axis and has a zero slope.
Image with alt text: In the Position versus Time graph, the horizontal axis is Time and the vertical axis is Position. The line begins at the origin and has a positive, linear slope. In the Velocity versus Time graph, the horizontal axis is Time and the vertical axis is Velocity. The line begins from the middle of the vertical axis and has a zero slope.

In the Position versus Time graph, the horizontal axis is Time and the vertical axis is Position. The line begins from the middle of the vertical axis and has a zero slope. In the Velocity versus Time graph, the horizontal axis is Time and the vertical axis is Velocity. The line begins at the origin and has a positive, linear slope.
Image with alt text: In the Position versus Time graph, the horizontal axis is Time and the vertical axis is Position. The line begins from the middle of the vertical axis and has a zero slope. In the Velocity versus Time graph, the horizontal axis is Time and the vertical axis is Velocity. The line begins at the origin and has a positive, linear slope.
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Answer 1

To determine which set of graphs illustrates identical motion patterns, we need to analyze the relationship between the position and velocity of the object.

1. Position vs. Time Graph:

   • A line with a positive, linear slope indicates that the object is moving away from the origin at a constant positive velocity.
   • A line with a negative, linear slope indicates that the object is moving towards the origin at a constant negative velocity.
   • A horizontal line (zero slope) means that the object is at rest (position is constant).

2. Velocity vs. Time Graph:

   • A line with a positive, linear slope indicates that the object's velocity is increasing positively over time (accelerating in the positive direction).
   • A line with a zero slope indicates that the object's velocity is constant.

Now, let's analyze the options:

• Option 1:

  • Position vs. Time: Negative slope (moving towards origin).
  • Velocity vs. Time: Positive slope (acceleration in the positive direction).
  • Not identical motion.

• Option 2:

  • Position vs. Time: Positive slope (moving away from origin).
  • Velocity vs. Time: Positive slope (accelerating in the positive direction).
  • Identical motion (both are moving positively).

• Option 3:

  • Position vs. Time: Positive slope (moving away from origin).
  • Velocity vs. Time: Zero slope (at rest).
  • Not identical motion.

• Option 4:

  • Position vs. Time: Zero slope (at rest).
  • Velocity vs. Time: Positive slope (acceleration).
  • Not identical motion.

Based on the analysis, Option 2 illustrates identical motion patterns for an object.