Carts D, E, and F start from rest on a frictionless, straight track at . Their…

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

Problem

Carts D, E, and F start from rest on a frictionless, straight track at

t = 0

. Their accelerations as functions of time for the interval

0 \le t \le 6\,\text{s}

are described below. • Cart D:

+4\,\text{m/s}^{2}

from

t=0

3\,\text{s}

, then

-2\,\text{m/s}^{2}

from

3\,\text{s}

6\,\text{s}

. • Cart E: constant

+1\,\text{m/s}^{2}

for the entire

6\,\text{s}

. • Cart F:

+6\,\text{m/s}^{2}

from

t=0

2\,\text{s}

, then

0\,\text{m/s}^{2}

from

2\,\text{s}

6\,\text{s}

. Which of the following ranks the speeds of the carts at

t = 6\,\text{s}

from greatest to least? (a)

D > F > E

(b)

E > F > D

(c)

F > D = E

(d)

F > D > E