Answer
(a) $\alpha = -1.25~rev/s^2$
The motor makes 23.3 revolutions.
(b) $t = 2.67~s$
Work Step by Step
(a) $\alpha = \frac{\omega_2-\omega_1}{t}$
$\alpha = \frac{(200~rev/60~s)-(500~rev/60~s)}{4.00~s}$
$\alpha = -1.25~rev/s^2$
Let $n$ be the number of revolutions.
$n = (500~rev/60~s)(4.00~s)+\frac{1}{2}~\alpha~t^2$
$n = (500~rev/60~s)(4.00~s)+\frac{1}{2}(-1.25~rev/s^2)(4.00~s)^2$
$n = 23.3~revolutions$
The motor makes 23.3 revolutions.
(b) $0 = (200~rev/60~s)-(1.25~rev/s^2)(t)$
$t = \frac{(200~rev/60~s)}{1.25~rev/s^2}$
$t = 2.67~s$
