The position of a bug crawling on a sheet is given by

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

Problem

r(t)=\langle \sin 3t,\;\ln(t^{2}+1)\rangle

, with

t

in seconds and coordinates in centimeters. Find the velocity components at

t=0.5\text{ s}

, expressing each component exactly.