The position of a particle in the plane is given by for

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

Problem

The position of a particle in the plane is given by

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

for

t\ge 0

. Determine all times

t

when the velocity and acceleration vectors are perpendicular.