On the interval

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

Problem

On the interval

0\le t\le 10

, a particle’s velocity satisfies •

v(t)>0

for

0<t<2

and

6<t<10

•

v(2)=v(6)=0

•

v(t)<0

for

2<t<6

Which statement about the particle’s motion best describes its change(s) in direction? (a) The particle reverses direction exactly once, at

t=6

, because velocity changes from negative to positive only there. (b) The particle never reverses direction because

v(t)

is positive for some

t

in every neighborhood of both

t=2

and

t=6

. (c) The particle reverses direction exactly twice, at

t=2

and

t=6

. (d) The particle reverses direction only at

t=2

because

v(t)

is negative immediately afterward and never becomes positive again.