Two cars leave the same intersection at

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

Problem

t=0

. Car A travels east with a speed (in mph) given by

v_A(t)=60+5t

, and Car B travels south with a speed given by

v_B(t)=40-2t

, where

t

is in hours (

0\le t\le4

). Find the instantaneous rate at which the distance between the two cars is changing when

t=2\text{ h}

. (a)

106\text{ mph}

(b)

70.0\text{ mph}

78.6\text{ mph}

(d)

72.1\text{ mph}