Mathematics

Problem

Consider the curve

x(t)=3t^{2}

and

y(t)=4t^{2}

for

0\le t\le 4

. Let

S

be the total distance traveled by the particle from

t=0

t=4

. At what time

t=t_{0}

(with

0<t_{0}<4

) has the particle traveled exactly

\tfrac12S

? a)

3

2\sqrt{2}

2

4^{2/3}