Consider the motion of a particle whose position vector is for

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

Problem

Consider the motion of a particle whose position vector is

\mathbf r(t)=\langle t\sin t,\,t\cos t\rangle

for

0\le t\le 2\pi

. For which of the following values of

t

are the velocity and acceleration vectors perpendicular? (a)

t=\dfrac{\pi}{2}

(b)

t=1

(c)

t=0

(d)

t=\pi