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).
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).
