Between and seconds

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Between

t=0

and

t=9

seconds, the velocity

v(t)

of a particle satisfies

v(t)\ge 0

[0,4]

and

v(t)\le 0

(4,9]

. The region above the

t

-axis and below the graph of

v

[0,4]

has area

15

(meter-seconds). The region below the

t

-axis and above the graph of

v

[4,9]

has area

6

(meter-seconds). What is

\displaystyle \frac{\int_{0}^{9} |v(t)|\,dt}{\int_{0}^{9} v(t)\,dt}

? (a)

\dfrac{15}{6}

(b) 1 (c)

\dfrac{7}{3}

(d)

\dfrac{5}{3}