a)
To find: The position
a)
Answer to Problem 51EP
The position vector of the particle is
Explanation of Solution
Given information: It is given that a particle moving along the graph
Formulas used: Suppose a particle moves along a smooth curve in the plane and its position at time
The position vector of the particle is
The velocity vector of the particle is
The acceleration of the particle is
Calculation:
The
Thus,
Substitute
Differentiate the equation
Substitute
Substitute 0 for
Since the particle moves along the graph of
Thus, the position of the particle is
b)
To find: The speed of the particle.
b)
Answer to Problem 51EP
The speed of the particle at the point
Explanation of Solution
Given information: It is given that a particle moving along the graph
Formulas used:
Suppose a particle moves along a smooth curve in the plane and its position at time
Calculation:
From part (a), the parametric equations for the particle path are
Substitute
Find the velocity of the particle at
The speed is the magnitude of the velocity. Find the speed of the particle at
Thus, the speed of the particle at the point
Chapter 10 Solutions
CALCULUS:GRAPHICAL,...,AP ED.-W/ACCESS
- 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