Q1 (99 points) Find the normal and tangential acceleration of the curve r(t) = e² i + tj + e¯¹ k, t Є R, at t = 0 in two ways: (A) by calculating the the dot product of the (vector) acceleration with the unit tangent and normal vectors; and (B) by calculating the rate of change of the speed, and the centripetal acceleration obtained from by the speed and the radius of curvature.

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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Q1 (99 points)
Find the normal and tangential acceleration of the curve
r(t) = e² i + tj + e¯¹ k, t Є R,
at t = 0 in two ways:
(A) by calculating the the dot product of the (vector) acceleration with
the unit tangent and normal vectors; and
(B) by calculating the rate of change of the speed, and the centripetal
acceleration obtained from by the speed and the radius of curvature.
Transcribed Image Text:Q1 (99 points) Find the normal and tangential acceleration of the curve r(t) = e² i + tj + e¯¹ k, t Є R, at t = 0 in two ways: (A) by calculating the the dot product of the (vector) acceleration with the unit tangent and normal vectors; and (B) by calculating the rate of change of the speed, and the centripetal acceleration obtained from by the speed and the radius of curvature.
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