Mathematics

Problem

For

0\le t\le 2

, a particle’s velocity vector is

\mathbf v(t)=\langle 3t^{2},\,4t\rangle

. What is the total distance the particle travels on this interval? a)

8\sqrt{2}

\dfrac{104\sqrt{13}+64}{27}

\dfrac{104\sqrt{13}-64}{27}

\dfrac{52\sqrt{13}-16}{9}