A particle’s position in meters is for s

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

Problem

A particle’s position in meters is

r(t)=\langle t^{3}-6t,\;4e^{2t}\rangle

for

t\ge 0

s. Determine both (i) the speed and (ii) the magnitude of the acceleration when

t=1\text{ s}

. Provide numerical values to three decimal places.