A car has wheels including the tire of radius OA 450 cm It a

A car has wheels (including the tire) of radius OA= 45.0 cm. It accelerates from rest to 40.0 mph = 17.9 m/s in 10 seconds. Calculate the angular acceleration of the wheels while the car is accelerating, assuming that the wheels rotate without slipping on the pavement. Calculate the number of revolutions through which the wheels rotate while the car is accelerating. The car comes to rest from 17.9 m/s with a uniform deceleration. During this deceleration, the wheels are observed to rotate through exactly 80 revolutions. How long does it take for the car to come to rest?

Solution

At a speed of 17.9 m/s the tyre is rotating = 17.9 / (2 pi * 45 * 10^-2)

= 6.331 revs/s = 39.78 rad/s

aceleration = w / t = 39.78 / 10

= 3.98 rad/s²

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Average speed during the 10 seconds = 6.331 / 2 = 3.1655 rps

number of revolutions in 10 s = 3.1655 * 10 = 31.65 revs

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It executes 80 revolutions at this average speed

time = 80 / 3.1655

= 25.27 s