(a)
To find: The average velocity of the particle at the given time intervals.
(a)
Answer to Problem 16E
The average velocity of the particle,
(i) At the interval [4, 8] is
(ii) At the interval [6, 8] is
(iii) At the interval [8, 10] is
(iv) At the interval [8, 12] is
Explanation of Solution
Given:
The displacement (in feet) of a particle moving in a straight line is
Formula used:
The average velocity over the time interval
Calculation:
Obtain the average velocity of the particle over the time interval
Take the position function
Simplify further and obtain the value of average velocity as follows.
Thus, the average velocity of the particle over the time interval
Section (i)
Obtain the average velocity of the particle over the time interval
Consider
Substitute
Thus, the average velocity of the particle over the time interval
Section (ii)
Obtain the average velocity of the particle over the time interval
Consider
Substitute
Thus, the average velocity of the particle over the time interval
Section (iii)
Obtain the average velocity of the particle over the time interval
Consider
Substitute
Thus, the average velocity of the particle over the time interval
Section (iv)
Obtain the average velocity of the particle over the time interval
Take
Substitute
Thus, the average velocity of the particle over the time interval
(b)
To find: The instantaneous velocity at
(b)
Answer to Problem 16E
The instantaneous velocity when
Explanation of Solution
Formula used:
The derivative
Calculation:
From part (a),
Use equation (2) to obtain the instantaneous velocity,
Therefore, the instantaneous velocity at
Substitute
Thus, the instantaneous velocity at
(c)
To sketch: The graph of the function
(c)
Explanation of Solution
Given:
The equation of the position function is
The secant lines whose slopes are the average velocities in part (a).
The tangent line whose slope is the instantaneous velocity in part (b).
Graph:
Use the online graphing calculator to draw the graph of the function
From the Figure 1, it is observed that the tangent line touches the curve at
Chapter 2 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