How to calculate angular speed?

[Romain Nzebele]

Homework Statement

A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s2after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.330 m? (b) What is the angular speed of the wheels when the car has traveled half the total distance?

Homework Equations

Theta=(omega0)t+(1/2)(alpha)(t^2)
avergealpha=(omegafinale-omegainitial)/time
averageacceleration= (Vf-Vo)/change in time

The Attempt at a Solution

For part (a)
First, I found the change in time by dividing 29 by 1.75 and obtained 16.57 s. Second, I multiplied the given acceleration by the radius to obtain the angular acceleration. I got -5.30rad/s^2. Third, I calculated theta using the above formula and I got 728.40 rads. Fourth, I divided 728.40 by 2pi and I got 115.9 revolutions.
For part (b)
First, I divided 16.57 seconds by two and got 8.285 seconds. Second I used the second formula above. I took omegafinale as 0 and time as 8.285 and calculated omegainitial to be 43.91 rad/s.

I got the right answer for part (a) but the textbook gives 62.1 rad/s for part (b). I don't understand how they got 62.1 rad/s as their answer. Can someone tell me what I did wrong in my reasoning or math? I will appreciate it very much.

 

[Doc Al]

First, I divided 16.57 seconds by two and got 8.285 seconds.

That's half the total time. But what you need is when half the distance is traveled.

 

[Romain Nzebele]

That's half the total time. But what you need is when half the distance is traveled.

But doesn't the car need half the time to travel half the distance since the deceleration is constant?

 

[Romain Nzebele]

That's half the total time. But what you need is when half the distance is traveled.

Oh, we don't have a constant speed in this case so we can't use half the time, right?

 

[Doc Al]

Oh, we don't have a constant speed in this case so we can't use half the time, right?

Exactly!

 

[Romain Nzebele]

Exactly!

Okay, thank you so very much.

 

[sojsail]

I multiplied the given acceleration by the radius to obtain the angular acceleration.

Just have to correct one error in the dialog above. You got the right answer for α, therefore what you did was DIVIDE the given acceleration by the radius. α = a/r

 

[Romain Nzebele]

Just have to correct one error in the dialog above. You got the right answer for α, therefore what you did was DIVIDE the given acceleration by the radius. α = a/r

Yes, that's right.