A particle moves such that its position vector where is a constant and is time

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

Problem

A particle moves such that its position vector

\vec{r}(t) = \cos \omega t \hat{i} + \sin \omega t \hat{j}

where

\omega

is a constant and

t

is time. Then which of the following statements is true for the velocity

\vec{v}(t)

and acceleration

\vec{a}(t)

of the particle: (1)

\vec{v}

is perpendicular to

\vec{r}

and

\vec{a}

is directed away from the origin (2)

\vec{v}

and

\vec{a}

both are perpendicular to

\vec{r}

(3)

\vec{v}

and

\vec{a}

both are parallel to

\vec{r}

(4)

\vec{v}

is perpendicular to

\vec{r}

and

\vec{a}

is directed towards the origin