Answer
$v(t)=-32t+24$
Work Step by Step
Define "up" as the positive direction of motion.
Acceleration is the derivative of velocity
$a(t)=v'(t)=-32\ \ \mathrm{f}\mathrm{t}/\mathrm{s}^{2}$
$v(t)=\displaystyle \int(-32)dt=-32t+C$
Given that $ v(0)=+24\qquad$(upward)
$24=-32(0)+C$
$C=24$
Thus,
$v(t)=-32t+24$
