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Exercise. Let C be a curve drawn by: p(t) = (2 cos(t), –-2 sin(t)) Find the length of the curve drawn by p as t runs from 0 to T: length = | ?

Exercise. Let C be a curve drawn by: p(t) = (2 cos(t), –-2 sin(t)) Find the length of the curve drawn by p as t runs from 0 to T: length = | ?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can u help me answer all three question please? Thank you.
Exercise. Let C be a curve drawn by: p(t) = (2 cos(t), –-2 sin(t)) Find the length of the curve drawn by p as t runs from 0 to T: length = 2. Exercise. The starting position of a particle is given by p(0) = (5, –2) Suppose the initial velocity is given by v(0) = (1,2) and the acceleration is given by a(t) = (2,3). Find: • The velocity function: v(t) = • The speed function: s(t) = • The position function: p(t) = 3 Exercise. The position vector for a particle is described by the vector-valued function: sin(at) for t > 0. Find (positive) a so the curve uses arc length as a parameter. a = 4 6
Transcribed Image Text:Exercise. Let C be a curve drawn by: p(t) = (2 cos(t), –-2 sin(t)) Find the length of the curve drawn by p as t runs from 0 to T: length = 2. Exercise. The starting position of a particle is given by p(0) = (5, –2) Suppose the initial velocity is given by v(0) = (1,2) and the acceleration is given by a(t) = (2,3). Find: • The velocity function: v(t) = • The speed function: s(t) = • The position function: p(t) = 3 Exercise. The position vector for a particle is described by the vector-valued function: sin(at) for t > 0. Find (positive) a so the curve uses arc length as a parameter. a = 4 6
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