r(t)
Definition
The position vector that describes an object's location in space as a function of time.
Analogy
Imagine you are playing a video game where you control a character moving around in a 3D world. The position vector r(t) would be like the coordinates that determine where your character is located at any given time. It tells you exactly where you are in relation to other objects or landmarks in the game.
Related terms
Velocity vector: The derivative of r(t), representing how fast an object is moving and its direction.
Acceleration vector: The derivative of velocity, showing how quickly an object's velocity is changing over time.
Parametric equations: Equations that describe curves using multiple variables, often including t as a parameter for time.
"r(t)" appears in:
Subjects (1)
Practice Questions (3)
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) = <3t^2 - t, 4t^3 + 2t>. At what time(s) is the particle moving in the direction of increasing y?
If a particle’s position vector is r(t) = ⟨cos(t), sin(t)⟩, what is its velocity vector?
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