A car accelerates uniformly from rest and reaches a speed of 22.7 m/s in 9.02 s. Assume the diameter of a tire is 58.5 cm. (a) Find the number of revolutions the tire makes during this motion, assuming that no slipping occurs. rev (b) What is the final angular speed of a tire in revolutions per second? rev/s

(a) The car is undergoing an acceleration of

so that in 9.02 s, it will have covered a distance of

The car has tires with diameter d = 58.5 cm = 0.585 m, and hence circumference π d ≈ 1.84 m. Divide the distance traveled by the tire circumference to determine how many revolutions it makes:

(b) The wheels have average angular velocity

where is the average angular velocity, and are the initial and final angular velocities (rev/s), and are the initial and final angular displacements (rev), respectively, and is the duration of the time between initial and final measurements. The second equality holds because acceleration is constant.

The wheels start at rest, so

a displacement distance is size of displ