The line segment from to is originally given by for

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

Problem

The line segment from

(0,0)

(15,20)

is originally given by

x=3t,\;y=4t

for

0\le t\le 5

. A student proposes the re-parameterization

x=\dfrac{3s}{5},\;y=\dfrac{4s}{5}

for

0\le s\le 25

. Verify that this new parameter

s

indeed measures arc length along the line by computing the speed under the new parameter.