The table shows the position of a motorcyclist after accelerating from rest.
(a) Find the average velocity for each tune period:
(i) [2, 4]
(ii) [3, 4]
(iii) [4, 5]
(iv) [4, 6]
(b) Use the graph of s as a function of t to estimate the instantaneous velocity when t = 3.
(a)
To find: The average velocity for given time periods.
Answer to Problem 7E
(i) The average velocity over the time interval [2, 4] is
(ii) The average velocity over the time interval [3, 4] is
(iii) The average velocity over the time interval [4, 5] is
(iv) The average velocity over the time interval [4, 6] is
Explanation of Solution
Formula used:
The average velocity over the time interval
Calculation:
Section-(i)
Obtain the average velocity over the time interval [2, 4].
Substitute
From the given table, it is observed that,
(i) When
(ii) When
Thus, the average velocity over the time interval [2, 4] is computed as follows.
Therefore, the average velocity over the time interval [2, 4] is
Section-(ii)
Obtain the average velocity over the time interval [3, 4].
Substitute
From the given table, it is observed that,
(i) When
(ii) When
Thus, the average velocity over the time interval [3, 4] is computed as follows.
Therefore, the average velocity over the time interval [3, 4] is
Section-(iii)
Obtain the average velocity over the time interval [4, 5].
Substitute
From the table, it is observed that,
(i) When
(ii) When
Thus, the average velocity over the time interval [4, 5] is computed as follows.
Therefore, the average velocity over the time interval [4, 5] is
Section-(iv)
Obtain the average velocity over the time interval [4, 6].
Substitute
From the table, it is observed that,
(i) When
(ii) When
Thus, the average velocity over the time interval [4, 6] is computed as follows.
Therefore, average velocity over the time interval [4, 6] is
(b)
To estimate: The instantaneous velocity when
Answer to Problem 7E
The estimated instantaneous velocity when
Explanation of Solution
Plot a curve using the points (0, 0), (1, 4.9), (2, 20.6), (3, 46.5), (4, 79.2), (5, 124.8) and (6, 176.7) as shown below in Figure 1.
Draw the slope of the tangent line at
The instantaneous velocity at
From Figure 2, the slope of the tangent line at (3, 46.5) is obtained below.
The estimated instantaneous velocity when
Chapter 2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
Additional Math Textbook Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Precalculus
Precalculus: A Unit Circle Approach
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