
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
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