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Vector-valued function

from class:

AP Calculus AB/BC

Definition

A vector-valued function is a mathematical function that takes one or more input variables and outputs a vector. In other words, it assigns a vector to each value of the input variable(s).

"Vector-valued function" also found in:

Subjects (6)

Practice Questions (20+)

A particle's position as a function of time (t) is given by the vector-valued function r(t) = <4t^2 - 5t, 2t^3 - t>. At what time(s) is the velocity of the particle equal to zero?
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <2t^2 + 3t, 4t^2 - 2t>. Find the acceleration vector-valued function, a(t), of the particle.
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <5t^3 - 2t, 6t^2 + 4t>. Find the acceleration vector-valued function, a(t), of the particle.
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <3t^3 - 4t, t^2 + 2t>. At what time(s) is the particle moving in the direction of increasing x?
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <4t^2 - t, 3t^2 + 2t>. At what time(s) is the particle slowing down at its maximum rate?
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <t^3 - 2t, 2t^2 + 3t>. Find the acceleration vector-valued function, a(t), of the particle.
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <3t^2 + t, 5t^3 - 2t>. Find the velocity vector-valued function, v(t), of the particle.
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <t^2 + 4t, 4t^3 - 3t>. Find the velocity vector-valued function, v(t), of the particle.
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <2t^3 + 5t, t^2 + 3t>. Find the acceleration vector-valued function, a(t), of the particle.
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <4t^3 - 3t, 2t^2 + t>. At what time(s) is the velocity of the particle equal to zero?
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <t^2 - 4t, 3t^3 + 2t>. Find the acceleration vector-valued function, a(t), of the particle.
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <2t^2 - 5t, t^2 + 3t>. At what time(s) is the particle slowing down at its maximum rate?
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <3t^2 - t, 4t^3 + 2t>. At what time(s) is the particle moving in the direction of increasing y?
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <t^3 + 2t, 6t^2 - 3t>. Find the acceleration vector-valued function, a(t), of the particle.
A particle's position as a function of time (t) is given by the vector-valued function r(t) = <7t^2 - 5t, 3t^3 - t>. At what time(s) is the velocity of the particle equal to zero?
How can we integrate a vector-valued function in AP Calculus?
What is the result of integrating a vector-valued function?
What is one common application of integrating a vector-valued function?
What does the indefinite integral of the acceleration vector-valued function with respect to time give us?
If a particle’s velocity is given by the vector-valued function r(t) = ⟨2t, t^2⟩, what is its acceleration vector?

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study guides for every class

that actually explain what's on your next test

Vector-valued function

from class:

AP Calculus AB/BC

Definition

"Vector-valued function" also found in:

Subjects (6)

Practice Questions (20+)

© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

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study guides for every class

that actually explain what's on your next test

Vector-valued function

from class:

AP Calculus AB/BC

Definition

Related terms

"Vector-valued function" also found in:

Subjects (6)

Practice Questions (20+)

© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

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