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Chapter 1: Problem 7

Keira starts at position \(x=23 \mathrm{m}\) along a coordinate axis. She then undergoes a displacement of \(-45 \mathrm{m} .\) What is her final position?

Short Answer

Expert verified
Keira's final position is \(68 \mathrm{m}\).

Step by step solution

01

Identify initial position

Keira's initial position is \(x = 23 \mathrm{m}\). This is given in the problem statement.
02

Understand the displacement

Keira's displacement is \(-45 \mathrm{m}\). This indicates a move in the opposite direction.
03

Calculate the final position

The final position is calculated by subtracting the displacement from the initial position. Therefore, the calculation is \[23 \mathrm{m} - (-45 \mathrm{m}) = 23 \mathrm{m} + 45 \mathrm{m} = 68 \mathrm{m}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Coordinate Axis
The concept of a coordinate axis is fundamental in understanding motion and displacement. Imagine it as a straight line that extends in two directions, like a number line in math class. It helps us determine positions in space.

Typically, the coordinate axis will have an origin, usually marked as 0, with positive numbers increasing in one direction and negative numbers in the opposite direction.
  • The right side of the origin is positive.
  • The left side of the origin is negative.
This setup allows you to precisely pinpoint and calculate movement changes, or displacements, of objects like Keira in this example.
Initial Position
The initial position is where the object starts. It is the starting point from which movement is measured. In the problem given, Keira's initial position is at 23 meters along the coordinate axis.

This initial value is crucial, because any further calculation or change in position will be compared against this starting point. For Keira to determine how far she has moved, you need to know where she began.
Final Position
The final position is the endpoint after the movement has occurred. It tells us where the object is located after undergoing a displacement.

To find Keira's final position, you use the initial position and add or subtract the displacement.
Here's how it works for Keira's scenario:
  • Initial position: 23 meters
  • Displacement: -45 meters
  • Final position: 23 - 45 = -22 meters
Thus, Keira ends up 22 meters in the negative direction from the origin.
Negative Displacement
Displacement refers to a change in position and can be positive or negative. When displacement is negative, it indicates movement in the opposite direction from the positive axis.

In Keira's example, her displacement is -45 meters, signaling a move 45 meters in the negative direction. This is different from distance, which is always positive and only measures how much ground has been covered regardless of direction.
  • Negative displacement: moves backward on the coordinate axis.
  • Positive displacement: moves forward.
Understanding this helps in interpreting motion and determining the resultant position efficiently.

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