Answer
$320\ \mathrm{f}\mathrm{t}/\mathrm{s}$ downward.
Work Step by Step
Define "up" as the positive direction of motion.
Acceleration is the derivative of velocity
$a(t)=v'(t)=-32\ \mathrm{f}\mathrm{t}/\mathrm{s}^{2}$
$v(t)=\displaystyle \int(-32)dt =-32t+C\ \mathrm{f}\mathrm{t}/\mathrm{s}$
To find C, use the given information: $v(0)=0$
$v(t)=-32t+C$
$0=0+\mathrm{C}$
$C=0$
Thus,
$v(t)=-32t\ \mathrm{f}\mathrm{t}/\mathrm{s}.$
After $t=10$ seconds,
$v(10)= -32(10) =-320\ \mathrm{f}\mathrm{t}/\mathrm{s}$
The stone is traveling $320\ \mathrm{f}\mathrm{t}/\mathrm{s}$ downward.
