Acceleration vector-valued function
Definition
An acceleration vector-valued function describes how quickly an object's velocity changes over time. It includes both magnitude and direction.
Analogy
Imagine riding a roller coaster where the acceleration vector-valued function tells you not only how fast your speed is changing but also in which direction you're being pushed.
Related terms
Velocity: Velocity is a vector quantity that describes an object's speed and direction of motion. It is calculated by dividing displacement by time taken.
Tangent Line: In calculus, the tangent line represents the instantaneous rate of change of a function at a specific point. For an acceleration vector-valued function, it represents the direction of motion at that point.
Second Derivative: The second derivative measures how the rate of change (derivative) itself changes with respect to another quantity. In the context of acceleration, it gives us information about jerk or changes in acceleration.
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Additional resources (1)
Practice Questions (5)
- 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) = <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) = <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) = <t^3 + 2t, 6t^2 - 3t>. Find the acceleration vector-valued function, a(t), of the particle.
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