I;m sorry, but I was stuck on the second part of this problem. Can you please help me?

An automobile engine slows down from 4500 rpm to 1500 rpm in 2.5 seconds.
a) calculate angular accceleration
b)calculate total number of revolutions done in this time.

What I did:
a) I got the answer, and it was right, and it was also negative, but: what confused me was b
b) It is decelerating, this really confused me. I wasn't even sure how to approach this.

average speed=4500+1500 divided by 2, or

average speed=3000 rpm

displacement=avgspeed*time
=3000rpm or 3000rev/3600sec *2.5sec
= 7500/3600 rev

I'm sorry, I tried this and got 2.1 and the computer keeps kicking it out as wrong. Your logic makes sense to me after I thought about it. Is there something I'm doing wrong?

wait never mind. There are only 60 seconds in a minute!

Of course, I'd be happy to help you with this problem!

Let's break down the problem step by step.

a) To calculate the angular acceleration, we'll use the formula:

Angular acceleration (α) = (Change in angular velocity) / (Change in time)

Given that the engine slows down from 4500 rpm (revolutions per minute) to 1500 rpm in 2.5 seconds, we can find the change in angular velocity by subtracting the final angular velocity from the initial angular velocity:

Change in angular velocity = Final angular velocity - Initial angular velocity

Change in angular velocity = 1500 rpm - 4500 rpm = -3000 rpm

Next, we need to convert the change in angular velocity from rpm to radians per second. Since 1 revolution is equal to 2π radians, we can convert the units as follows:

Change in angular velocity (in radians per second) = (Change in angular velocity in rpm) * (2π radians / 1 revolution) * (1 minute / 60 seconds)

Substituting the values, we have:

Change in angular velocity (in radians per second) = -3000 rpm * (2π radians / 1 revolution) * (1 minute / 60 seconds)

Simplifying this, we get:

Change in angular velocity (in radians per second) ≈ -314.16 rad/s

Finally, we can calculate the angular acceleration using the formula mentioned earlier:

Angular acceleration (α) = (-314.16 rad/s) / (2.5 s)

Solving this, we find:

Angular acceleration (α) ≈ -125.66 rad/s^2

Note that the negative value indicates that the engine is decelerating.

b) To calculate the total number of revolutions done in this time, we can use the formula:

Total number of revolutions = (Change in angular velocity) / (Initial angular velocity)

Given that the change in angular velocity is -3000 rpm and the initial angular velocity is 4500 rpm, we can substitute these values into the formula:

Total number of revolutions = (-3000 rpm) / (4500 rpm)

Calculating this, we find:

Total number of revolutions ≈ -0.67 revolutions

Again, the negative value indicates that the engine is decelerating and not completing a full revolution.

I hope this explanation helps you understand how to approach and solve the problem. Let me know if you have any further questions!