Answer
$310\ \ \mathrm{f}\mathrm{t}/\mathrm{s}$ downward.
Work Step by Step
Define "up" as the positive direction of motion.
Acceleration is the derivative of velocity
$a(t)=v'(t)=-32\ \ \mathrm{f}\mathrm{t}/\mathrm{s}^{2}$
$v(t)=\displaystyle \int(-32)dt=-32t+C.$
To find C, use the given information: $v(0)=10$
$v(t)=-32t+C$
$10=0+\mathrm{C}$
$C=10$
Thus,
$v(t)=-32t+10 \ \ \mathrm{f}\mathrm{t}/\mathrm{s}$
After 10 seconds,
$v(10)=-32(10)+10=-310$
The stone is traveling $310\ \ \mathrm{f}\mathrm{t}/\mathrm{s}$ downward.
