The initial angular speed of the wheels of the car is $omega_{i} = 5.2 mathrm{~rad/s}$. The final angular speed of the wheels of the car is $omega_{f} = 7.9 mathrm{~rad/s}$. Time time interval that the wheels of the car takes to increase the speed is $Delta t = 1.3 mathrm{~s}$.

$textbf{Required: }$

Finding the angular acceleration of the wheels.

As the textbook mentions, the average angular acceleration is given by the change in angular velocity within a given time interval

$$
begin{align*}
alpha_{avg} &= dfrac{ Delta omega }{ Delta t } \
&= dfrac{ omega_{f} – omega_{i} }{Delta t } \
&= dfrac{ 7.9 mathrm{~rad/s} – 5.2 mathrm{~rad/s} }{ 1.3 mathrm{~s} } \
&= 2.077 mathrm{~rad/s^{2}}
end{align*}
$$

So, the average angular acceleration of the wheels is $2.077 mathrm{~rad/s^{2}}$.

The initial angular speed of the bicycle’s wheels is $omega_{i} = 0 mathrm{~rad/s}$. The angular acceleration of the bicycle is $alpha = 2.3 mathrm{~rad/s^{2}}$. The time interval that the bicycle takes to reach to the final angular speed is $alpha = 3.8 mathrm{~s}$.

$textbf{Required: }$

Finding the final angular speed of the wheels.

As the textbook mentions, the average angular acceleration is given by the change in angular velocity within a given time interval

$$
begin{align*}
alpha_{avg} &= dfrac{ Delta omega }{ Delta t } \
&= dfrac{ omega_{f} – omega_{i} }{Delta t } \
&= dfrac{ omega_{f} – 0 mathrm{~rad/s} }{Delta t } \
&= dfrac{ omega_{f} }{Delta t } \
end{align*}
$$

Rearrange and solve for the final angular speed of the wheels:

$$
begin{align*}
omega_{f} &= alpha_{avg} ~ Delta t \
&= 2.3 mathrm{~rad/s^{2}} times 3.8 mathrm{~s} \
&= 8.74 mathrm{~rad/s}
end{align*}
$$

So, the final angular speed of the wheels is $8.74 mathrm{~rad/s}$.