Concept explainers
(a)
To find: The velocity and the acceleration function.
(a)
Explanation of Solution
Given: The expression coordinate of particle is
Velocity is the derivation of the first position.
So, the expression for velocity is calculated as:
Acceleration is the second derivative of position. So,
Therefore, the velocity function is
(b)
To find: When the particle is moving upward and when it is moving downward.
(b)
Explanation of Solution
Given: The expression coordinate of particle is
Velocity is the derivation of the first position.
So, the expression for velocity is calculated as:
Equate the above equation to zero.
Plugging in the values lesser and greater than
Therefore, the particle is moving downward from the time
(c)
To find: The distance that the particle travels in the time interval.
(c)
Explanation of Solution
Given: The expression coordinate of particle is
Velocity is the derivation of the first position.
So, the expression for velocity is calculated as:
Equate the above equation to zero.
To find the total distance, break up the position function into two intervals
Hence,
(d)
To graph : The position, velocity and the acceleration function.
(d)
Explanation of Solution
Given: The expression coordinate of particle is
The graph of position, velocity and the acceleration function on a single plane is shown in figure below.
Figure (1)
Therefore, the graph of position, velocity and the acceleration function on a single plane is shown in Figure (1).
(e)
To graph : When the particle is speeding up and speeding down..
(e)
Explanation of Solution
Given: The expression coordinate of particle is
The graph of position, velocity and the acceleration function on a single plane is shown in figure below.
Figure (1)
From the graph both the acceleration and velocity have the same sign after
Hence, the particle is speeding up during
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced 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