A particle satisfies for every value of in its domain
MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices
Problem
A particle satisfies r(t)⋅r′(t)=0 for every value of t in its domain. Which statement best describes what this condition implies about the particle’s path?
(a) The particle’s speed is constant because ∣r′(t)∣ is constant.
(b) The particle’s acceleration is always perpendicular to its position vector because r(t)⋅r′′(t)=0.
(c) The particle moves along a sphere centered at the origin because ∣r(t)∣ is constant.
(d) The particle moves in a straight line since r′(t) is always perpendicular to r(t).