Mathematics

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

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

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

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