Homework Help is Here – Start Your Trial Now!
Math
Calculus
In the equations of the image below, what does the ds stand for?

In the equations of the image below, what does the ds stand for?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question

In the equations of the image below, what does the ds stand for?

Tangential and Normal Components of Acceleration When an object is accelerated by gravity, brakes, or rocket motors, we often need to know how much of the acceleration acts in the direction of motion, which is the direction of the tangent vector T. We can calculate this using the Chain Rule to rewrite v as a = = = -T+ V= Then we differentiate both ends of this string of equalities to get d²s dt² dr dt d.s dt ds dt -T+K = 2 ds (1) ²N. dt dr ds ds dt ds dT dv d ds d²s = = -T+ dt² - (¹) - ¹ + de de (Td²) = dt dt dt dt dt d² s dT ds ds d² s = T+ dt² dt² = T ds dt dt ds (KN d₂) dt dT ds = KN
Transcribed Image Text:Tangential and Normal Components of Acceleration When an object is accelerated by gravity, brakes, or rocket motors, we often need to know how much of the acceleration acts in the direction of motion, which is the direction of the tangent vector T. We can calculate this using the Chain Rule to rewrite v as a = = = -T+ V= Then we differentiate both ends of this string of equalities to get d²s dt² dr dt d.s dt ds dt -T+K = 2 ds (1) ²N. dt dr ds ds dt ds dT dv d ds d²s = = -T+ dt² - (¹) - ¹ + de de (Td²) = dt dt dt dt dt d² s dT ds ds d² s = T+ dt² dt² = T ds dt dt ds (KN d₂) dt dT ds = KN
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS