1. Consider the path of a moving object described by 7(t) = (cos? t, sin? t,t) -25 sts 2 (a) Find v(t) and i (). (b) Find T(t) and T (-). (c) Find the speed at t =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 33E
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1. Consider the path of a moving object described by
7(t) = (cos? t, sin? t,t)
-25 <t<2
(a) Find i(t) and i (:).
(b) Find T(t) and T :).
(c) Find the speed at t =.
(d) At what time(s) t during the time interval [-.25,2] is the object farthest
from the origin?
(e) At what time(s) t during the time interval [-.25,2] is the object closest to
the origin?
(f) At what time(s) t during the time interval [-.25,2] does the object achieve
maximum speed?
(g) At what time(s) t during the time interval [-.25,2] is the speed of the
object a minimum?
(h) At what time(s) does the object intersect one of the coordinate axes?
(i) At what time(s) does the object intersect one of the coordinate planes?
Transcribed Image Text:1. Consider the path of a moving object described by 7(t) = (cos? t, sin? t,t) -25 <t<2 (a) Find i(t) and i (:). (b) Find T(t) and T :). (c) Find the speed at t =. (d) At what time(s) t during the time interval [-.25,2] is the object farthest from the origin? (e) At what time(s) t during the time interval [-.25,2] is the object closest to the origin? (f) At what time(s) t during the time interval [-.25,2] does the object achieve maximum speed? (g) At what time(s) t during the time interval [-.25,2] is the speed of the object a minimum? (h) At what time(s) does the object intersect one of the coordinate axes? (i) At what time(s) does the object intersect one of the coordinate planes?
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