The density (in kg/m ) of material along a rod depends on position (in m) through a…

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The density

\rho

(in kg/m

^{3}

) of material along a rod depends on position

x

(in m) through a differentiable, invertible function

\rho=h(x)

. At

x=4

m, measurements give

\rho=7

kg/m

^{3}

and

\dfrac{d\rho}{dx}=-0.5

kg/m

^{3}

per m. The position of a particle on the rod is given by

x=s(t)

with

s(2)=4

and

\dfrac{dx}{dt}=0.8

m/s at

t=2

s. What is

\dfrac{dt}{d\rho}

\rho=7

kg/m

^{3}

? (a)

-1.25\;\text{s}\!/\!(\text{kg}/\text{m}^{3})

(b)

2.5\;\text{s}\!/\!(\text{kg}/\text{m}^{3})

(c)

-2.5\;\text{s}\!/\!(\text{kg}/\text{m}^{3})

(d)

-0.625\;\text{s}\!/\!(\text{kg}/\text{m}^{3})