Two cars P and Q start from a point at the same time in a straight line and their…

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

Problem

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by

X_P(t) = at + bt^2

and

X_Q(t) = ft - t^2

. At what time do the cars have the same velocity? (a)

\frac{a+f}{2(1+b)}

(b)

\frac{f-a}{2(1+b)}

(c)

\frac{a-f}{1+b}

(d)

\frac{a+f}{2(b-1)}