A particle moves in space with position vector for .

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

Problem

A particle moves in space with position vector

\mathbf r(t)=\langle t^{3}-3t,\,t^{2},\,2t\rangle

for

t\ge 0

. (a) Determine all times

t

when the velocity and acceleration vectors are orthogonal. (b) At

t=2

, state whether the particle’s speed is increasing or decreasing.