For , a curve is given by and , where is a constant. If the length of the curve on…

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

Problem

For

0\le t\le 1

, a curve is given by

x(t)=kt

and

y(t)=\dfrac{k}{2}t^{2}

, where

k>0

is a constant. If the length of the curve on this interval is

3

, determine the value of

k

(express your answer exactly).