5 seconds expired during the deceleration.
Top rotated 45 radians during these 5 seconds.
First, calculate the chance in velocity, by subtracting the initial velocity from the final velocity. So
6 rad/s - 12 rad/s = -6 rad/s
So we lost a total of 6 rad/s. Divide that by the deceleration to give the number of seconds. So
-6 rad/s / -1.2 rad/s^2 = 5 s
So it takes 5 seconds for the deceleration to happen.
The equation that expresses the number of radians performed under constant deceleration with an initial velocity is
d = VT + 0.5 AT^2
where
d = distance
V = initial velocity
T = time
A = acceleration
Substituting the known values gives.
d = VT + 0.5 AT^2
d = 12 rad/s * 5s + 0.5 * -1.2 rad/s^2 (5s)^2
d = 60 rad -0.6 rad/s^2 *25s^2
d = 60 rad -15 rad
d = 45 rad
So the top rotated 45 radians while decelerating from 12 rad/s to 6 rad/s
