a.
To calculate: The instantaneous velocity.
a.
Answer to Problem 21E
The instantaneous velocity is
Explanation of Solution
Given information:
The function is
Concept used:
The formula used is
Calculation:
The function is
Differentiate the function with respect to time
Conclusion: The instantaneous velocity of the particle is
b.
To calculate: The acceleration of the particle.
b.
Answer to Problem 21E
The acceleration of the particle is
Explanation of Solution
Given information:
The function is
Concept used:
The formula used is
Calculation:
The function is
Differentiate the function with respect to time
Differentiate the function again with respect to time
Conclusion: The acceleration of the particle is
c.
To calculate: The time at which the particle is at rest.
c.
Answer to Problem 21E
The times when particle is at rest are
Explanation of Solution
Given information:
The function is
Concept used:
The particle will be in rest when the velocity of the particle becomes zero.
Calculation:
The function is
Differentiate the function with respect to time
Equate the velocity to zero.
Solve further.
Conclusion: The particle will be in rest when
d.
To calculate: The time when particle changes its direction.
d.
Explanation of Solution
Given information:
The function is
Calculation:
The function is
The graph of the function is shown below.
The motion of the particle can be divided into four phases
(a) The particle starts when
(b) The particle stops at
(c) The particle changes direction and continues its motion until at
(d) Then it stops and continues its motion.
Chapter 2 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
- 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