/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 5 A person walks first at a consta... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 5

A person walks first at a constant speed of 5.00 \(\mathrm{m} / \mathrm{s}\) along a straight line from point \(A\) to point \(B\) and then back along the line from \(B\) to \(A\) at a constant speed of 3.00 \(\mathrm{m} / \mathrm{s}\) . What is (a) her average speed over the entire trip? (b) her average velocity over the entire trip?

Short Answer

Expert verified
The average speed over the entire trip is 3.75 m/s and the average velocity is 0 m/s.

Step by step solution

01

Identify Variables & Find Distance

First, identify the given variables: speed from A to B is 5.00 m/s, and speed from B to A is 3.00 m/s. Assumed is that the distance from A to B equals the distance from B to A. Let's denote this distance as 'd'. Because speed is distance over time, we can express the time it takes to travel from A to B as t_{AB} = d / 5.00 m/s and from B to A as t_{BA} = d / 3.00 m/s.
02

Calculate Total Distance

To find the total distance traveled, simply add the distance from A to B and from B to A: Total Distance = d + d = 2d.
03

Calculate Total Time

The total time of travel (t_{total}) is the sum of the time it takes to travel from A to B and the time to return from B to A. Calculate this using the formulas for t_{AB} and t_{BA}: t_{total} = t_{AB} + t_{BA} = d/5.00 + d/3.00 = (3d + 5d) / 15.00 = 8d / 15.00.
04

Calculate Average Speed

The average speed is the total distance traveled divided by the total time. Using the total distance and total time obtained from previous steps: Average Speed = (2d) / (8d / 15.00) = (2d * 15.00) / (8d) = 30.00 / 8 = 3.75 m/s.
05

Determine Displacement

Displacement is the change in position from the start point to the end point. Since the traveler returns to the starting point A, the displacement is 0 m.
06

Calculate Average Velocity

Average velocity is the total displacement divided by the total time. Since the displacement is 0 m, the average velocity is 0 m/s regardless of how much time has passed.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Constant Speed
When an object travels at a constant speed, it covers equal distances in equal intervals of time. This means that the speed does not change over the duration of the motion. For example, if a car is moving with a constant speed of 60 km/h on a highway, it would cover 60 kilometers every hour without speeding up or slowing down.

In the exercise, the person walks from point A to point B at a constant speed of 5.00 m/s, which is quite straightforward. This simplifies calculations as we don't have to take into account any acceleration or deceleration. The concept of constant speed is fundamental to understanding uniform motion and plays a key role in problems related to distance and time.
Displacement
Displacement, a vector quantity, refers to an object's overall change in position. It's not just about how far the object has traveled, but also in what direction. To compute displacement, you draw a straight line from the starting point to the final point, regardless of the path taken to get there.

In our exercise, the person walks from point A to B and then back to A. Here's the catch: despite traveling a certain distance during the round trip, the displacement is zero because the person ends up where they started. This is a key aspect of displacement that differentiates it from distance; displacement can be zero after a round trip, but the distance traveled is always a positive value.
Average Velocity
Average velocity is defined as the total displacement divided by the total time taken to travel that displacement. It is a vector quantity, which means it has both magnitude and direction. Since velocity accounts for direction, if an object returns to its starting point, its displacement is zero and consequently, its average velocity is also zero.

This principle is neatly illustrated in the exercise where, despite the person walking at constant speeds to and from point B, the average velocity for the entire trip is 0 m/s because the starting and ending points are the same, resulting in zero displacement. Understanding this concept helps underscore the difference between velocity (which includes direction) and speed (which does not).

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A car is approaching a hill at 30.0 \(\mathrm{m} / \mathrm{s}\) when its engine suddenly fails just at the bottom of the hill. The car moves with a constant acceleration of \(-2.00 \mathrm{m} / \mathrm{s}^{2}\) while coasting up the hill. (a) Write equations for the position along the slope and for the velocity as functions of time, taking \(x=0\) at the bottom of the hill, where \(v_{i}=30.0 \mathrm{m} / \mathrm{s}\) . (b) Determine the maximum distance the car rolls up the hill.

Draw motion diagrams for (a) an object moving to the right at constant speed, (b) an object moving to the right and speeding up at a constant rate, (c) an object moving to the right and slowing down at a constant rate, (d) an object moving to the left and speeding up at a constant rate, and (e) an object moving to the left and slowing down at a changes in speed were not uniform; that is, if the speed were not changing at a constant rate?

For many years Colonel John P. Stapp, USAF, held the world's land speed record. On March \(19,1954\) , he rode a rocket-propelled sled that moved down a track at a speed of 632 \(\mathrm{mi} / \mathrm{h}\) . He and the sled were safely brought to rest in 1.40 \(\mathrm{s}\) (Fig. P2.31). Determine (a) the negative acceleration he experienced and (b) the distance he traveled during this negative acceleration.

A jet plane lands with a speed of 100 \(\mathrm{m} / \mathrm{s}\) and can accelerate at a maximum rate of \(-5.00 \mathrm{m} / \mathrm{s}^{2}\) as it comes to rest. (a) From the instant the plane touches the runway, what is the minimum time interval needed before it can come to rest? (b) Can this plane land on a small tropical island airport where the runway is 0.800 \(\mathrm{km}\) long?

Kathy tests her new sports car by racing with Stan, an experienced racer. Both start from rest, but Kathy leaves the starting line \(1.00 \mathrm{~s}\) after Stan does. Stan moves with a constant acceleration of \(3.50 \mathrm{~m} / \mathrm{~s}^{2},\) while Kathy maintains an acceleration of \(4.90 \mathrm{~m} / \mathrm{~s}^{2}\). Find (a) the time at which Kathy overtakes Stan, (b) the distance she travels before she catches him, and (c) the speeds of both cars at the instant Kathy overtakes Stan.
See all solutions

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Read Explanation

Geometrical and Physical Optics

Read Explanation

Electromagnetism

Read Explanation

Electricity and Magnetism

Read Explanation

Fundamentals of Physics

Read Explanation

Linear Momentum

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.