Let describe the position of a particle for

MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Let r(t)=⟨5cos⁡t,5sin⁡t⟩\mathbf r(t)=\langle 5\cos t,5\sin t\rangle describe the position of a particle for 0≤t≤2π0\le t\le 2\pi, where tt is measured in seconds and distances are in meters. (a) Show that the particle moves with constant speed and state that constant value. (b) Compute the total distance traveled by the particle on 0≤t≤2π0\le t\le 2\pi. (c) Find the displacement vector of the particle for the same time interval. (d) Explain why the answers to parts (b) and (c) differ, relating your explanation to the geometry of the path.

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