Question

Suppose you start at the position \(x_{\mathrm{i}}=7.5 \mathrm{~m}\). If you undergo a displacement of \(-8.3 \mathrm{~m}\), what is your final position?

Short answer

The final position is \(-0.8 \mathrm{~m}\).

Step-by-step solution

Recognize the Formula

In order to find the final position, recognize that the position change (or displacement) can be calculated using:\[ x_{\mathrm{f}} = x_{\mathrm{i}} + \Delta x \]where \( x_{\mathrm{f}} \) is the final position, \( x_{\mathrm{i}} \) is the initial position, and \( \Delta x \) is the displacement.

Substitute Given Values

Substitute the known values into the formula:\[ x_{\mathrm{f}} = 7.5\, \text{m} + (-8.3\, \text{m}) \]

Perform the Calculation

Carry out the arithmetic operation:\[ x_{\mathrm{f}} = 7.5 - 8.3 = -0.8\, \text{m} \]

Interpret the Result

The result means that the final position, \( x_{\mathrm{f}} \), is \(-0.8\, \text{m}\). This implies a move to the left on the number line, indicating a shift into the negative space compared to the starting point.

Key concepts

Initial Position

In physics, when we talk about an object's initial position, we refer to the point where the object begins its motion. It's essentially the starting line for the object's journey. This is a crucial concept because knowing where an object starts helps us understand the entire context of its movement and calculate other important values, such as displacement and final position.

The initial position is often denoted by the symbol \( x_i \). In our exercise, the initial position is given as \( 7.5 \, \text{m} \). This means that the object begins at 7.5 meters along a particular direction, which we can think of as a point on a number line.

• Serves as the starting reference point
• Helps in determining whether an object has moved forward or backward
• Used in formulas to calculate movement or changes in position

Understanding the initial position enables one to predict and analyze the path and speed of an object as it proceeds through space and time.

Final Position

The final position of an object in physics is where it ends its journey or comes to a stop. Once we know both the initial position and the displacement, it becomes possible to easily calculate this final position.

In the formula \( x_f = x_i + \Delta x \), \( x_f \) stands for the final position. This tells us where the object is located after it has moved from its initial position. In our exercise, the calculated final position was \( -0.8 \, \text{m} \), showing that the object has moved into negative space.

• Marked as \( x_f \) in calculations
• Shows the end location of the object
• Can change based on the displacement value, indicating shifts to the left or right

By finding the final position, we can understand how far and in what direction the object has traveled, making it a vital part of understanding motion in physics.

Arithmetic Operations in Physics

Arithmetic operations are essential tools in physics for solving problems about motion, forces, energy, and more. They involve basic math skills that help interpret and analyze data effectively. In the context of the given problem, arithmetic operations help us manage the concepts of displacement and position.

The key operation in our exercise is addition, used to find the final position \( x_f \). However, when dealing with negative displacement, it acts more like a subtraction. Thus, performing \( 7.5 - 8.3 \) correctly gave the result of \( -0.8 \, \text{m} \).

• Addition and subtraction help determine changes in position
• Critical for calculating vectors and shifts in movement
• Ensure accurate interpretation of results through proper calculation

Understanding arithmetic operations in physics enables students to solve diverse problems with confidence, focusing on the correct procedures and ensuring results make physical sense.