Mathematics

Problem

A curve

C

is described by the vector function

\mathbf r(t)

for

0\le t\le5

. A second parameterization of the same path is given by

\mathbf s(u)=\mathbf r(2u)

for

0\le u\le2.5

. Which statement best describes the relationship between the arc lengths of the two parameterizations over their stated intervals? a) The arc length of

\mathbf s

is twice the arc length of

\mathbf r

. (

2L_{r}

) b) The two arc lengths are equal. c) The arc length of

\mathbf s

is half the arc length of

\mathbf r

. (

\tfrac12L_{r}

) d) The arc length of

\mathbf s

is one–quarter the arc length of

\mathbf r

. (

\tfrac14L_{r}

)

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