Question

Running on a \(50-\mathrm{m}\) by 40 -m rectangular track, you complete one lap in \(100 \mathrm{~s}\). What is your average velocity for the lap?

Short answer

Answer: The average velocity of the person running one lap around the rectangular track is 0 m/s.

Step-by-step solution

Understand the problem and given information

The first step is understanding the problem and the information provided. The runner completes one lap around the rectangular track with dimensions 50 m x 40 m, and it takes them 100 seconds to do so. We need to find their average velocity during this lap.

Calculate the total displacement

Since velocity is a vector quantity, we need to determine the total displacement, which is a vector representing the change in position. After completing one lap, the runner ends up at their starting point. Thus, the total displacement is 0.

Calculate the average velocity

To find the average velocity, we divide the total displacement by the time it takes to complete one lap. In this case, the total displacement is 0, and the time taken is 100 seconds. The formula for average velocity is: Average Velocity = Total Displacement / Time In this case: Average Velocity = 0 / 100 = 0 m/s

Express the result

The average velocity of the runner completing one lap around the rectangular track is 0 m/s. Since the runner ends up at their starting point, the overall change in position is 0, resulting in an average velocity of 0 m/s.

Key concepts

Displacement in Physics

Displacement is a fundamental concept in physics that represents the overall change in an object's position. It's a vector quantity, meaning it has both magnitude and direction. To imagine displacement, think of it as the shortest path between the starting and ending points. Unlike distance, which accounts for the total length of the path travelled regardless of direction, displacement only considers the initial and final positions.

For example, when you walk around a rectangular track and finish exactly where you started, your displacement is zero. This is because your starting and ending points are the same, and the shortest path between these two points is non-existent or has no length. This is crucial in understanding problems in physics when calculating values like velocity, which relies on displacement rather than total distance covered.

Vector Quantities Essential Understanding

Vector quantities are not just numbers; they are numbers with direction. This makes them distinctly different from scalar quantities, which are numbers with magnitude only, like distance or speed. Understanding vector quantities is essential in physics because they provide a more complete description of physical phenomena.

In the context of our runner on the track, even though they move a substantial distance, the displacement vector quantity is zero because their starting and ending positions are identical. Other examples of vector quantities include force, acceleration, and momentum. Each of these not only has a size or magnitude but also a direction, which is fundamental to accurately describing motion and solving physics problems.

Physics Problem Solving Strategies

Solving physics problems can be quite challenging, but adopting a structured approach can simplify the process. Here are some problem-solving strategies:

• Understanding the Problem: Clearly define what is being asked. Identify the given information and what you need to find.
• Visual Representation: Sketching diagrams can help visualize the problem, especially in mechanics where motion and forces are involved.
• Applying Physics Principles: Determine which physics concepts and equations are relevant to the problem. In the track problem, understanding vector quantities like displacement is crucial.
• Mathematical Solution: Carry out calculations using the relevant equations, keeping in mind units and significant figures.
• Interpreting the Result: Make sure the solution makes sense in the context of the physical situation. In our previous example, an average velocity of 0 m/s reflects that there's no net displacement over one lap of the track.

Adopting these strategies enhances your ability to solve physics problems accurately and effectively.