Unit 12.1–12.3: Vector-Valued Functions, Velocity, Acceleration

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Last updated 10:08 PM on 6/4/26
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13 Terms

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Vector-valued function

r(t)=⟨f(t),g(t),h(t)⟩

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Derivative of vector function

r'(t)=⟨f',g',h'⟩

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Integral of vector function

Integrate each component separately.

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Velocity vector

v(t)=r'(t)

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Acceleration vector

a(t)=r''(t)

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Speed

|v(t)|

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Position from velocity

r(t)=∫v(t)dt+C

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Tangent line

r=r(t₀)+r'(t₀)(t-t₀)

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How to find speed

Take magnitude of velocity.

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How to find acceleration

Differentiate velocity.

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How to find position from acceleration

Integrate twice.

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Professor trick

Speed is a scalar, velocity is a vector.

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Common mistake

Confusing speed with velocity.