* (b) Suppose that I is an interval and r(t) = (x(t), y(t), z(t)), where t I, is a twice-differentiable curve that describes the position of an object in R³. If the object is moving at a constant speed, show that its velocity is always perpendicular to its acceleration.
* (b) Suppose that I is an interval and r(t) = (x(t), y(t), z(t)), where t I, is a twice-differentiable curve that describes the position of an object in R³. If the object is moving at a constant speed, show that its velocity is always perpendicular to its acceleration.
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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Question
Please solve part(b) only. Thx.
Transcribed Image Text:6. (a) Let I be an interval and
Ti(t) = (x₁(t), y₁ (t), 2₁ (t)) and F₂(t) = (x₂ (t), y₂2(t), Z₂ (t)),
where t = I, be two differentiable curves in R³
Show that
i.
ii.
d
·(F₁(t) · r₂(t)) = r²'₁(t) · F₂(t) + r₁(t) · r²¹₂ (t)
dt
d
(F₁(t) × F₂(t)) = r₁(t) × F₂2(t) + F₁ (t) × √₂ (t)
dt
(b) * Suppose that I is an interval and
r(t) = (x(t), y(t), z(t)),
where t€ I, is a twice-differentiable curve that describes the position of an
object in R³.
If the object is moving at a constant speed, show that its velocity is always
perpendicular to its acceleration.
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