(a)
To calculate: The magnitude of the velocity
(a)
Answer to Problem 50E
The required magnitude of the velocity vector is 32.985.
Explanation of Solution
Given information:
The position of the particle:
Calculation:
The given position of the particle is
It is known that for a position vector
So,
Now,
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
Substitute
Substitute 4 for t in the above expression.
Hence, the required magnitude of the velocity vector is 32.985.
(b)
To calculate: The total distance traveled by the particle from
(b)
Answer to Problem 50E
The required total distance is 46.062.
Explanation of Solution
Given information:
The position of the particle:
Calculation:
The given position of the particle is
It is known that for a position vector
So,
Now,
The velocity of the particle which moves along a path is
To find the total distance traveled by the particle, use the formula
So,
Hence, the required total distance is 46.062.
(c)
To calculate: The value of
(c)
Answer to Problem 50E
The required value of
Explanation of Solution
Given information:
The position of the particle:
Calculation:
The given position of the particle is
Rewrite the x -component as:
Substitute
Differentiate the above expression with respect to x .
Hence, the required value of
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic
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