A curve is described by the vector function for

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

Problem

A curve CC is described by the vector function r(t)\mathbf r(t) for 0≤t≤50\le t\le5. A second parameterization of the same path is given by s(u)=r(2u)\mathbf s(u)=\mathbf r(2u) for 0≤u≤2.50\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 s\mathbf s is twice the arc length of r\mathbf r. ( 2Lr2L_{r} ) (b) The two arc lengths are equal. (c) The arc length of s\mathbf s is half the arc length of r\mathbf r. ( 12Lr\tfrac12L_{r} ) (d) The arc length of s\mathbf s is one–quarter the arc length of r\mathbf r. ( 14Lr\tfrac14L_{r} )

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