For a particle with position vector and velocity

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

Problem

For a particle with position vector

r(t)

and velocity

v(t)=r'(t)

, which of the following conditions must hold on an interval if and only if the particle moves with constant speed on that interval? (a)

v'(t)=0

(b)

|v(t)|^{2}=0

(c)

\dfrac{d}{dt}\bigl(|v(t)|^{2}\bigr)=0

(d)

r(t)\cdot v(t)=0