(a)
To calculate: The velocity and speed of the particle when
(a)
Answer to Problem 37E
The required velocity and speed of the particle are
Explanation of Solution
Given information:
The position
Calculation:
Consider the position vector be
So,
It is known that for a position vector
So,
Substitute
Also, it is known that the magnitude of the velocity vector of a particle is known as the speed of the particle.
The magnitude of a vector
At
Hence, the required velocity and speed of the particle are
(b)
To graph: The path of the particle.
(b)
Explanation of Solution
Given information:
The position vector of the particle:
Calculation:
Consider the position vector be
So,
It is known that for a position vector
So,
Substitute
Also, it is known that the magnitude of the velocity vector of a particle is known as the speed of the particle.
The magnitude of a vector
At
Thus, the velocity and speed of the particle are
The graph of the path of the particle is shown below:
(c)
To determine: Whether the particle is moving to the left or to the right when
(c)
Answer to Problem 37E
The particle is moving to the right when
Explanation of Solution
Given information:
The position vector of the particle:
Calculation:
Consider the position vector be
So,
It is known that for a position vector
So,
Substitute
Also, it is known that the magnitude of the velocity vector of a particle is known as the speed of the particle.
The magnitude of a vector
At
Thus, the velocity and speed of the particle are
The graph of the path of the particle is shown below:
From the above graph, it is seen that the particle is moving to the right when
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
Additional Math Textbook Solutions
Precalculus
University Calculus: Early Transcendentals (3rd Edition)
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