Can you please help me explain with this rotation problem

A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 53 rad/s. The wheel is run at that angular velocity for 40 s and then power is shut off. The wheel decelerates uniformly at 2.2 rad/s2 until the wheel stops. In this situation, the total number of revolutions made by the wheel is closest to:

answer is correct @Jim, only units are wrong. It's radian, not revolution.
Let's solve it though:

Let's say: Initial angular speed = ω(0)
Final angular speed = ω
Number of revoultion = θ
Time = t
angular acceleration = α (alpha)

Case I: When machine is started,
ω(0) = 0, ω = 53 rad/sec, t=10sec, θ = ?, α = ?

Using ω = ω(0) + αt
--> α = 53/10 = 5.3 rad/sec^2

Next, using θ = ω(0)t + 0.5αt^2
--> θ = 0.5*5.3*100 = 265 radians = 265/2π revolutions ...let this be (1)....

Case II
ω(0) = 53 rad/sec, ω = 53 rad/sec, t=40sec, θ = ?, α = 0

Directly using θ = ω(0)t + 0.5αt^2
--> θ = 53*40 = 2120 radians = 2120/2π revolutions....let this be (2)...

Case III
ω(0) = 53 rad/sec, ω = 0 rad/sec, t=?, θ = ?, α = (-2.2) rad/sec^2

Using ω = ω(0) + αt
--> 53/2.2 = t
--> t =24 sec (approx.)

Using θ = ω(0)t + 0.5αt^2
--> θ = 53*24 - 0.5*2.2*576
--> θ = 639 radians (approx.) = 639/2π revolutions ...let this be (3)...

Total revolutions = (1) + (2) +(3) = 3024/2π = 482 revolutions (approx.)

EDIT: Answer 2 --> In first 10 seconds, it moves 265 radians. Since we need to find average velocity till 25 seconds, it will move (53*15) =795 radians for 15 seconds.
So, average velocity= total revolution/total time = (795+265)/25 = 1060/25 = 42.4 rad/sec.

I'll show you the method, you can plug in the numbers...

This is a three part problem, 1) Constant acceleration 2) Constant velocity 3) Constant deceleration