Cars and travel along a straight highway

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Cars

X

and

Y

travel along a straight highway. Their positions (in kilometers) at time

t

hours are

s_X(t)=t^2+2t

and

s_Y(t)=12t-t^2

, respectively, for

0\le t\le 5

. At what time in this interval are the two cars farthest apart? (a)

2\text{ h}

(b)

4\text{ h}

(c)

2.5\text{ h}

(d)

3\text{ h}