Concept explainers
a.
To find : Velocity of the particle.
a.
Answer to Problem 28E
The velocity of the function is
Explanation of Solution
Given information :
The position function of the particle is
Calculation :
Since, the first derivative of the position function gives velocity. Therefore,
Find the first derivative to get the velocity of the particle:
Hence,
The velocity of the function is
b.
To find : Acceleration of the particle.
b.
Answer to Problem 28E
The acceleration of the function is
Explanation of Solution
Given information :
The position function of the particle is
Calculation :
Since, the second derivative of the position function gives acceleration. Therefore,
Find the second derivative to get the velocity of the particle:
Hence,
The acceleration of the function is
c.
To describe : The motion of the particle.
c.
Answer to Problem 28E
The particle is moving to the right on interval
Explanation of Solution
Given information :
The position function of the particle is
Calculation :
From part (a) velocity is
When the function
Set
The zero partitions the t axis into two intervals as shown in the sign graph of v below:
The particle is moving to the right on interval
Set
Therefore, at
Hence,
The particle is moving to the right on interval
Chapter 5 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus & Its Applications (14th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning