For the motion defined by and (with measured in radians)

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

Problem

For the motion defined by

r=2\theta

and

\theta=t

(with

t

measured in radians), what is the speed of the particle at

t=\dfrac{\pi}{2}

? (a)

\pi

(b)

\sqrt{\pi^{2}+4}

(c)

\pi\sqrt{2}

(d)

\sqrt{5}