$x_i$

Definition

$x_i$ is a variable that represents the position of an object at a specific point in time. It is a fundamental concept in the study of position, displacement, and average velocity, as it allows us to quantify and analyze the movement of objects in one-dimensional space.

5 Must Know Facts For Your Next Test

1. $x_i$ is a scalar quantity, meaning it has a magnitude but no direction.
2. The subscript $i$ in $x_i$ indicates that the position is measured at a specific time or index, allowing for the analysis of an object's motion over time.
3. Changes in $x_i$ over time can be used to calculate an object's displacement and average velocity.
4. The initial position of an object is often represented as $x_0$, and subsequent positions are denoted as $x_1$, $x_2$, and so on.
5. Understanding the relationship between $x_i$, displacement, and average velocity is crucial for solving problems involving one-dimensional motion.

Review Questions

• Explain how the variable $x_i$ is used to describe the position of an object.
  • The variable $x_i$ represents the position of an object at a specific point in time. It is a scalar quantity that allows us to quantify the location of an object along a one-dimensional coordinate system. By tracking changes in $x_i$ over time, we can calculate the object's displacement and average velocity, which are essential for understanding and analyzing one-dimensional motion.
• Describe the relationship between $x_i$, displacement, and average velocity.
  • The variable $x_i$ is directly related to an object's displacement and average velocity. Displacement is the change in an object's position, calculated as the difference between the final position ($x_f$) and the initial position ($x_0$). Average velocity is the rate of change of an object's position over a given time interval, determined by dividing the displacement by the time elapsed. Understanding the connections between $x_i$, displacement, and average velocity is crucial for analyzing and solving problems involving one-dimensional motion.
• Analyze how the subscript $i$ in $x_i$ is used to track changes in an object's position over time.
  • The subscript $i$ in $x_i$ indicates that the position is measured at a specific time or index. This allows us to track the changes in an object's position as it moves through one-dimensional space. For example, $x_0$ represents the initial position, $x_1$ represents the position at the next time step, $x_2$ represents the position at the following time step, and so on. By analyzing the changes in $x_i$ over time, we can determine the object's displacement and calculate its average velocity, which are essential for understanding and predicting the object's motion.

Related terms

Position: The location of an object in space, typically measured relative to a reference point or coordinate system.

Displacement: The change in an object's position from one point to another, measured as the straight-line distance between the two points.

Average Velocity: The rate of change of an object's position over a given time interval, calculated as the displacement divided by the time elapsed.