(a)
To find: The velocity and acceleration at time t.
(a)
Answer to Problem 35E
The velocity of smooth level surface is
The acceleration of smooth level surface is
Explanation of Solution
Given:
The equation of motion is
Derivative rule:
Constant Multiple Rule:
If c is constant and
Recall:
If
If
Calculation:
Obtain the velocity at time t.
Apply the Constant Multiple Rule as shown in equation (1),
Thus, the velocity of
Obtain the acceleration at time t.
Apply the Constant Multiple Rule as shown in equation (1),
Therefore, the acceleration of
(b)
To find: The position, velocity and acceleration at
(b)
Answer to Problem 35E
The position, velocity and acceleration at
The direction of the particle is moving to the left (negative direction).
Explanation of Solution
Given:
The equation of motion is
Calculation:
The position
Thus, the position
From part (a), the velocity of
The velocity
Thus, the velocity
From part (a), the acceleration of
The acceleration
Thus, the acceleration
Here, the velocity of the particle at
This implies that, the velocity of the particle at
Therefore,the direction of the particle is moving to the left (negative direction).
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- 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