A car starts from rest and covers a distance of 22.0 m while accelerating at a constant rate of 2.6 m/s2. If the radius of the car wheels is 26.0 cm, what is the final angular speed (in rad/s) of the car wheels?

Hint: If you're unsure where to start, think about how you would find the final speed of the car first.

To find the final angular speed of the car wheels, we can first find the final linear speed of the car using the equation of motion:

v^2 = u^2 + 2as

Where:
v = final linear speed
u = initial linear speed (which is 0 m/s in this case, since the car starts from rest)
a = acceleration
s = distance

Rearranging the equation to solve for v, we have:

v^2 = 0^2 + 2(2.6 m/s^2)(22.0 m)
v^2 = 0 + 114.4 m^2/s^2
v = √(114.4 m^2/s^2)
v = 10.7 m/s (rounded to one decimal place)

Now that we have the final linear speed (v) of the car, we can find the final angular speed (ω) of the car wheels using the equation:

v = ωr

Where:
v = linear speed
ω = angular speed
r = radius of the car wheels

Rearranging the equation to solve for ω, we have:

ω = v / r
ω = 10.7 m/s / 0.26 m (converting the radius from centimeters to meters)
ω = 41.2 rad/s (rounded to one decimal place)

Therefore, the final angular speed of the car wheels is 41.2 rad/s.