Answer the questions below about the concepts of velocity and speed for motion in the…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Answer the questions below about the concepts of velocity and speed for motion in the plane. Assume all component functions are differentiable on an open interval containing t=c.
(a) Describe clearly the distinction between the velocity vector of a particle and the particle’s speed at a given instant.
(b) Suppose a particle’s velocity vector is v(c)=⟨0,0⟩ at an isolated instant t=c. Explain whether t=c must represent a local extremum of the particle’s speed. Support your conclusion with reasoning that references differentiability and appropriate definitions, but without explicit computation for a particular function.