Consider the parametric curve and for

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

Problem

Consider the parametric curve

x(t)=t^{2}

and

y(t)=\dfrac{t^{3}}{3}

for

0\le t\le T

. If the arc length of the curve on this interval equals

5

, determine the value of

T

(express your answer exactly).