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Calculus 3: Vector function

Calculus 3: Vector function

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...
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Calculus 3: Vector function

A particle is moving in the space with the position at time t is modelled by the vector function R(t) = cos(t)i + sin(t)j + 3tk . Find the velocity, acceleration, the speed and direction ㅠ of motion of the particle at time t = 4 Solution The velocity at time t: V(t) = R' (t) = =< The velocity at time t = π 7: V() = R(7) 4 The acceleration at time t: A(t) = R" (t) =< π 4 : 4 ( 7 ) = R'" ( The acceleration at time t = The direction at time t = ㅠ The speed at time t = | ||V ( 7 ) || = ||R² ( 7 ) || = ㅠ 4 = [ V() ||||||
Transcribed Image Text:A particle is moving in the space with the position at time t is modelled by the vector function R(t) = cos(t)i + sin(t)j + 3tk . Find the velocity, acceleration, the speed and direction ㅠ of motion of the particle at time t = 4 Solution The velocity at time t: V(t) = R' (t) = =< The velocity at time t = π 7: V() = R(7) 4 The acceleration at time t: A(t) = R" (t) =< π 4 : 4 ( 7 ) = R'" ( The acceleration at time t = The direction at time t = ㅠ The speed at time t = | ||V ( 7 ) || = ||R² ( 7 ) || = ㅠ 4 = [ V() ||||||
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