The position of a particle is

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

Problem

\mathbf r(t)=\langle t^{3},\, 3t^{2}-6t,\,4\rangle

. For what value of

t

in the interval

0\le t\le 2

are the velocity and acceleration vectors perpendicular? (a)

t=1

(b)

t\approx0.77\;(\text{the real root of }t^{3}+2t-2=0)

(c)

t=\sqrt{\dfrac{2}{3}}

(d) There is no such

t

in the interval.