A particle moves in a plane such that its position vector is r (t)=3 ( t) i +3 ( t) j…

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

Problem

A particle moves in a plane such that its position vector is

\mathbf{r}(t)=3 \cos (\pi t) \hat{\mathbf{i}}+3 \sin (\pi t) \hat{\mathbf{j}}

for

t

in seconds. Find the velocity vector

\mathbf{v}(t)

and its magnitude.