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After its journey to the head, arms, and legs, a round trip distance of about \(3 \mathrm{m},\) the red blood cell returns to the left ventricle after 1 minute. What is the average velocity for the trip? A. \(0.05 \mathrm{m} / \mathrm{s},\) downward B. \(0.5 \mathrm{m} / \mathrm{s},\) downward C. \(0 \mathrm{m} / \mathrm{s},\) round trip D. 0.05 \(\mathrm{m} / \mathrm{s}\) , upward

Short Answer

Expert verified
C. 0 m/s, round trip.

Step by step solution

01

Understand Average Velocity

The average velocity is calculated as the total displacement divided by the total time taken. It is a vector quantity and provides the direction of motion over time.
02

Determine Total Displacement

For a round trip, the object returns to its initial position. Thus, the total displacement, which is the net change in position, is zero meters because displacement is calculated as final position minus initial position.
03

Find the Time of the Trip

The problem states that the round trip takes 1 minute. Therefore, the time is 1 minute, or 60 seconds.
04

Calculate Average Velocity

Use the formula for average velocity: \( v_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}} \). Substituting the values we have, \( v_{avg} = \frac{0 \text{ m}}{60 \text{ s}} = 0 \text{ m/s} \).
05

Determine the Correct Answer

According to the calculations, the average velocity for the trip is \(0 \text{ m/s}\). The correct option that matches this result is C, which states \(0 \text{ m/s}\), round trip.

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Key Concepts

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

Displacement
Displacement is essential when trying to understand motion, especially in physics problems like the one about the round trip of a red blood cell. Displacement refers to the change in position of an object. It is not the total distance traveled, but rather the straight line distance from the starting point to the ending point, considering direction as well.
It's important to note that since displacement is dependent on the initial and final positions, for a round trip—where an object starts and ends at the same location—the displacement equals zero. This is because the starting and ending positions are the same, meaning there's no net change in position. In the mentioned red blood cell exercise, though the blood cell traveled three meters, the displacement is zero as it returned to its starting point.
Vector Quantity
In physics, quantities can be classified as either scalars or vectors. Vectors are crucial in understanding quantities like displacement and velocity. Unlike scalars that have only magnitude, vectors have both magnitude and direction.
This means when discussing vector quantities, it isn't enough to simply mention a number; the direction is equally important. For instance, in the exercise, the average velocity is a vector quantity. It has a magnitude (numerical value) and a direction (even if it's zero, the direction is relevant when non-zero). In the context of the exercise, since the displacement was zero, the vector's magnitude was zero, making the direction irrelevant.
Here are some key points about vector quantities:
  • They are represented with an arrow sign where the length denotes magnitude, and the direction of the arrow denotes the direction.
  • Examples include displacement, velocity, acceleration, and force.
  • Vectors help in solving physics problems that involve direction, making them integral to understanding motion.
Physics Problem Solving
Physics problem solving often involves a methodical approach that starts with understanding the problem itself. Here is how to tackle such a problem, exemplified in the exercise:
  • **Understand the Concept:** Know the definitions and relevant formulas, like average velocity being total displacement over total time.
  • **Identify Given Information:** Extract all the data provided, such as total distance, displacement, time, and direction manifestations.
  • **Calculate using Formulas:** For instance, in the exercise, using the average velocity formula led to the determination that it was 0 m/s.
  • **Verify the Solution:** Ensure your final answer makes logical sense within the context of the problem and choose the correct one from available options.
Being systematic and breaking down each part of the problem ensures a clear understanding and accurate solution.
Kinematics
Kinematics is a branch of physics that explains the motion of objects without considering the causes behind the motion. It's part of mechanics and deals primarily with quantities like displacement, velocity, and time.
In the exercise about the red blood cell, kinematics is demonstrated through the understanding of motion over a timeframe of one minute and covering a distance. Displacement, a key term in kinematics, and its correlation with time and velocity, is a focus of the solution. This highlights how kinematic principles apply to real-world physical problems by simplifying complex motions into understandable terms through straightforward calculations. Remember, kinematics tackles the "how" of motion, enabling predictions and analyses of real-world movements by breaking them down mathematically.

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On a 20 -mile bike ride, you ride the first 10 miles at an average speed of 8 \(\mathrm{mi} / \mathrm{h}\) . What must your average speed over the next 10 miles be to have your average speed for the total 20 miles be (a) 4 \(\mathrm{mi} / \mathrm{h} ?\) (b) 12 \(\mathrm{mi} / \mathrm{h} ?\) (c) Given this average speed for the first 10 miles, can you possibly attain an average speed of 16 \(\mathrm{mi} / \mathrm{h}\) for the total \(20-\) mile ride? Explain.

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