Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
6th Edition
ISBN: 9781418300203
Author: Prentice Hall
Publisher: Prentice Hall
Question
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Chapter 2.4, Problem 9E

a.

To determine

To calculate: The value of time when the particle moves forward, backward, increase in speed, decrease in speed.

a.

Expert Solution
Check Mark

Answer to Problem 9E

The particle moves forward from t=0 sec to t=1 sec , from t=5 sec to t=6 sec, moves backward from t=1 sec to t=5 sec , speed of particle increase from t=3 sec to t=6 sec and speed of particle decreases from t=0 sec to t=2 sec, t=6 sec to t=7 sec.

Explanation of Solution

Given information:

The graph of the velocity verses time

  Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020, Chapter 2.4, Problem 9E , additional homework tip 1

Concept used:

The displacement of the particle is final distance minus initial distance.

Calculation:

When the particle is in positive y axis then the particle will move forward and when the particle is in negative y axis the particle will move backwards.

In the given graph, the particle is in positive y axis from t=0 sec to t=1 sec , from t=5 sec to t=6 sec.

In the given graph, the particle is in positive y axis from t=1 sec to t=5 sec.

When the slope is positive that is the line is moving upward from left to right then the speed of the particle will increase and if the slope is negative that is line is moving downwards from left to right then the speed of the particle will decrease.

The slope of the line is positive from t=3 sec to t=6 sec, the speed of the particle increases.

The slope of the line is negative from t=0 sec to t=2 sec, t=6 sec to t=7 sec, the speed of the particle decreases.

Conclusion: The particle moves forward from t=0 sec to t=1 sec , from t=5 sec to t=6 sec, moves backward from t=1 sec to t=5 sec , speed of particle increase from t=3 sec to t=6 sec and speed of particle decreases from t=0 sec to t=2 sec, t=6 sec to t=7 sec.

b.

To determine

To calculate: The time when acceleration is positive, negative and constant.

b.

Expert Solution
Check Mark

Answer to Problem 9E

The time of positive acceleration is from t=3 sec to t=6 sec, negative acceleration from t=0 sec to t=2 sec, t=6 sec to t=7 sec and zero acceleration from t=2 sec to t=3 sec and from t=7 sec to t=9 sec.

Explanation of Solution

Given information:

The graph of the velocity verses time

  Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020, Chapter 2.4, Problem 9E , additional homework tip 2

Calculation:

When the slope is positive, then the acceleration will be positive.

The acceleration of the particle is positive from t=3 sec to t=6 sec.

When the slope is negative, then the acceleration will be negative.

The acceleration of the particle is negative from t=0 sec to t=2 sec, t=6 sec to t=7 sec.

The acceleration of the particle will be zero when the velocity is constant.

So the acceleration will be constant from t=2 sec to t=3 sec and from t=7 sec to t=9 sec.

Conclusion: The time of positive acceleration is from t=3 sec to t=6 sec, negative acceleration from t=0 sec to t=2 sec, t=6 sec to t=7 sec and zero acceleration from t=2 sec to t=3 sec and from t=7 sec to t=9 sec.

c.

To determine

To calculate: The greatest speed of the particle.

c.

Expert Solution
Check Mark

Answer to Problem 9E

The value of time is t=0 sec and from t=2 sec to t=3 sec.

Explanation of Solution

Given information:

The graph of velocity verses time is shown below.

  Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020, Chapter 2.4, Problem 9E , additional homework tip 3

Concept used:

The speed is always a positive quantity.

Calculation:

The speed is greatest at t=0 sec and from t=2 sec to t=3 sec.

Conclusion: The value of time is t=0 sec and from t=2 sec to t=3 sec.

d.

To determine

To calculate:. The value of time

d.

Expert Solution
Check Mark

Answer to Problem 9E

The time is from t=7 sec to t=9 sec.

Explanation of Solution

Given information:

The function is st=t2−3t+2 and time is t=4

Calculation:

The particle is standing still from t=7 sec to t=9 sec.

Conclusion: The time is from t=7 sec to t=9 sec.

Previous
Chapter 2.4, Problem 8E
Next
Chapter 2.4, Problem 10E

Chapter 2 Solutions

Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020

Ch. 2.1 - Prob. 1QRCh. 2.1 - Prob. 2QRCh. 2.1 - Prob. 3QRCh. 2.1 - Prob. 4QRCh. 2.1 - Prob. 5QRCh. 2.1 - Prob. 6QRCh. 2.1 - Prob. 7QRCh. 2.1 - Prob. 8QRCh. 2.1 - Prob. 9QRCh. 2.1 - Prob. 10QR
Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10ECh. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.2 - Prob. 1QRCh. 2.2 - Prob. 2QRCh. 2.2 - Prob. 3QRCh. 2.2 - Prob. 4QRCh. 2.2 - Prob. 5QRCh. 2.2 - Prob. 6QRCh. 2.2 - Prob. 7QRCh. 2.2 - Prob. 8QRCh. 2.2 - Prob. 9QRCh. 2.2 - Prob. 10QRCh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.2 - Prob. 43ECh. 2.2 - Prob. 44ECh. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.3 - Prob. 1QRCh. 2.3 - Prob. 2QRCh. 2.3 - Prob. 3QRCh. 2.3 - Prob. 4QRCh. 2.3 - Prob. 5QRCh. 2.3 - Prob. 6QRCh. 2.3 - Prob. 7QRCh. 2.3 - Prob. 8QRCh. 2.3 - Prob. 9QRCh. 2.3 - Prob. 10QRCh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 49ECh. 2.3 - Prob. 50ECh. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Prob. 55ECh. 2.3 - Prob. 56ECh. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 59ECh. 2.3 - Prob. 1QQCh. 2.3 - Prob. 2QQCh. 2.3 - Prob. 3QQCh. 2.3 - Prob. 4QQCh. 2.4 - Prob. 1QRCh. 2.4 - Prob. 2QRCh. 2.4 - Prob. 3QRCh. 2.4 - Prob. 4QRCh. 2.4 - Prob. 5QRCh. 2.4 - Prob. 6QRCh. 2.4 - Prob. 7QRCh. 2.4 - Prob. 8QRCh. 2.4 - Prob. 9QRCh. 2.4 - Prob. 10QRCh. 2.4 - Prob. 1ECh. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Prob. 6ECh. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Prob. 47ECh. 2.4 - Prob. 48ECh. 2.4 - Prob. 49ECh. 2.4 - Prob. 50ECh. 2.5 - Prob. 1QRCh. 2.5 - Prob. 2QRCh. 2.5 - Prob. 3QRCh. 2.5 - Prob. 4QRCh. 2.5 - Prob. 5QRCh. 2.5 - Prob. 6QRCh. 2.5 - Prob. 7QRCh. 2.5 - Prob. 8QRCh. 2.5 - Prob. 9QRCh. 2.5 - Prob. 10QRCh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Prob. 35ECh. 2.5 - Prob. 36ECh. 2.5 - Prob. 37ECh. 2.5 - Prob. 38ECh. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 48ECh. 2.5 - Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 1QQCh. 2.5 - Prob. 2QQCh. 2.5 - Prob. 3QQCh. 2.5 - Prob. 4QQCh. 2 - Prob. 1RWDTCh. 2 - Prob. 2RWDTCh. 2 - Prob. 3RWDTCh. 2 - Prob. 4RWDTCh. 2 - Prob. 5RWDTCh. 2 - Prob. 6RWDTCh. 2 - Prob. 7RWDTCh. 2 - Prob. 8RWDTCh. 2 - Prob. 9RWDTCh. 2 - Prob. 10RWDTCh. 2 - Prob. 1RECh. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Prob. 77RECh. 2 - Prob. 78RECh. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Prob. 81EPCh. 2 - Prob. 82EPCh. 2 - Prob. 83EP
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