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Calculus 3
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This document is a collection of detailed lecture notes from a university-level course on Multivariable Calculus and Physics. It covers essential topics including lines, planes, and surfaces, projectile motion, limits, partial derivatives, optimization, and integration techniques in various coordin...

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  • August 18, 2024
  • 37
  • 2024/2025
  • Class notes
  • Daniel ingebretson
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Math 210 Lecture 5: Projectile motion and
arc length

Daniel Ingebretson

University of Illinois at Chicago


July 21, 2024

,Position, velocity, acceleration
Let r(t) = ⟨x(t), y (t), z(t)⟩ be the position of a particle in
R3 at time t.

,Position, velocity, acceleration
Let r(t) = ⟨x(t), y (t), z(t)⟩ be the position of a particle in
R3 at time t.
Its velocity at time t is v(t) = r′ (t) = ⟨x ′ (t), y ′ (t), z ′ (t)⟩, and
its speed is
q
|v′ (t)| = x ′ (t)2 + y ′ (t)2 + z ′ (t)2 .

, Position, velocity, acceleration
Let r(t) = ⟨x(t), y (t), z(t)⟩ be the position of a particle in
R3 at time t.
Its velocity at time t is v(t) = r′ (t) = ⟨x ′ (t), y ′ (t), z ′ (t)⟩, and
its speed is
q
|v′ (t)| = x ′ (t)2 + y ′ (t)2 + z ′ (t)2 .

Its acceleration is a(t) = v′ (t) = r′′ (t).

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