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Particle

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AP Calculus AB/BC

Definition

A particle refers to a small object or point that is used to represent the position of an object in space.

"Particle" also found in:

Subjects (2)

Practice Questions (5)

A particle moves on the xy-plane. The y-coordinate of its position is described by the function y(t) = 8t^2 + 10t + 7. And, the x-coordinate of its position is described by the function x(t) = -5(t - 5)^3. Evaluate the first derivative of the y-coordinate with respect to the x-coordinate, dy/dx, at time t = 1.
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 moves along a curve in the plane with a velocity vector given by v(t) = ⟨2t, 4t^3⟩. If the particle’s initial position is ⟨1, 4⟩, what is the position vector of the particle at time t = 2?
A particle moves along a curve defined by the parametric equations x = 3t^2 and y = 2t^3. What is the approximate distance traveled by the particle from time t = 0 to t = 2?
A particle moves along a curve defined by the parametric equations x = t^3 and y = t^2. What is the acceleration vector of the particle at time t = 2?

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