A particle starts from rest at position on a straight line and is attracted toward…

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

Problem

A particle starts from rest at position

x=x_{0}>0

on a straight line and is attracted toward the origin by a force that produces acceleration

a(x)=-\dfrac{k}{x^{2}}

, where

k>0

is a constant and

x

is measured in meters. Which expression gives the particle’s speed

v

when it has reached position

x

(

0<x<x_{0}

)? (a)

v(x)=\sqrt{\,2k\!\left(\dfrac{1}{x_{0}}-\dfrac{1}{x}\right)}

(b)

v(x)=\sqrt{\,2k\!\left(\dfrac{1}{x}-\dfrac{1}{x_{0}}\right)}

(c)

v(x)=\sqrt{\,k\!\left(\dfrac{1}{x}-\dfrac{1}{x_{0}}\right)}

(d)

v(x)=\sqrt{\,k\!\left(\dfrac{1}{x}+\dfrac{1}{x_{0}}\right)}