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a. Find the velocity and speed of the object. b. Find the acceleration of the object. 30. r(t) = ( +1, t² + 10t), for t > 0 %3D 3

a. Find the velocity and speed of the object. b. Find the acceleration of the object. 30. r(t) = ( +1, t² + 10t), for t > 0 %3D 3

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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25-27. Finding r from r' Find the function r that satisfies the given conditions. 25. r'(t) = (1, sin 2t, sec? t); r(0) = (2, 2, 2) 26. r'(t) = (e', 2e2", 6e); r(0) = (1, 3,-1) 4. 27. r'(t) 2t+1, 3t2 2); r(1) = (0, 0, 0) %3D 1+t2 28-29. Unit tangent vectors Find the unit tangent vector T(t) for the following parameterized curves. Then determine the unit tangent vector at the given value of t. 28. r(t) = (8, 3 sin 2t, 3 cos 2t), for 0 <t < T; t = n/4 29. r(t) = (2e', e2", t), for 0 <t < 27; t = 0 30-31. Velocity and acceleration from position Consider the following position functions. a. Find the velocity and speed of the object. b. Find the acceleration of the object. 30. r(t): +1, + 10t for t > 0 31. r(t) = (c"+ 4t +1 for t> 0 32-33. Solving equations of motion Given an acceleration vector, initial velocity (uo, vo), and initial position (xo, Yo), find the velocity and position vectors for t 0. 32. a(t) = (1, 4), (40, vo) = (4, 3), (æ0, Yo) = (0, 2) 33. a(t) = (cos t, 2 sin t), (uo, vo) = (2, 1), (xo, yo) = (1, 34. T Orthogonal r and r' Find all points on the ellipse r(t) = (1, 8 sin t, cos t), for 0<t< 2n, at which r(t) and r'(t) are orthogonal. Sketch the curve and the tangent vectors to verify your conclusion. T 35-36. Modeling motion Consider the motion of the following objects, Assume the x-axis is horizontol tli
Transcribed Image Text:25-27. Finding r from r' Find the function r that satisfies the given conditions. 25. r'(t) = (1, sin 2t, sec? t); r(0) = (2, 2, 2) 26. r'(t) = (e', 2e2", 6e); r(0) = (1, 3,-1) 4. 27. r'(t) 2t+1, 3t2 2); r(1) = (0, 0, 0) %3D 1+t2 28-29. Unit tangent vectors Find the unit tangent vector T(t) for the following parameterized curves. Then determine the unit tangent vector at the given value of t. 28. r(t) = (8, 3 sin 2t, 3 cos 2t), for 0 <t < T; t = n/4 29. r(t) = (2e', e2", t), for 0 <t < 27; t = 0 30-31. Velocity and acceleration from position Consider the following position functions. a. Find the velocity and speed of the object. b. Find the acceleration of the object. 30. r(t): +1, + 10t for t > 0 31. r(t) = (c"+ 4t +1 for t> 0 32-33. Solving equations of motion Given an acceleration vector, initial velocity (uo, vo), and initial position (xo, Yo), find the velocity and position vectors for t 0. 32. a(t) = (1, 4), (40, vo) = (4, 3), (æ0, Yo) = (0, 2) 33. a(t) = (cos t, 2 sin t), (uo, vo) = (2, 1), (xo, yo) = (1, 34. T Orthogonal r and r' Find all points on the ellipse r(t) = (1, 8 sin t, cos t), for 0<t< 2n, at which r(t) and r'(t) are orthogonal. Sketch the curve and the tangent vectors to verify your conclusion. T 35-36. Modeling motion Consider the motion of the following objects, Assume the x-axis is horizontol tli
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