A curve in the plane is described by the position vector for .

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

Problem

A curve in the plane is described by the position vector

\mathbf r(t)=\langle t^{3},\,3t^{2}\rangle

for

0\le t\le 1

. (a) Determine the exact length of the curve from

t=0

t=1

. (b) Compute a three-decimal-place approximation of your answer in part (a) and interpret this value in the context of the particle’s motion.