A car accelerates uniformly such that its speed increases from 36 km/h to 108 km/h in 10 s. If the radius of its wheels is 2 m, how many revolutions does each wheel complete during this time? Assume no slipping.

Step-by-step solution

Initial linear speed, u = 36 km/h = 36 5 18 = 10 m/s Final linear speed, v = 108 km/h = 108 5 18 = 30 m/s Distance covered by the car in t = 10 s is given by the average velocity multiplied by time: s = ( u + v 2 ) t = ( 10 + 30 2 ) 10 = 200 m In pure rolling, the linear distance covered by the center of mass is equal to the distance rolled by the wheel along its circumference. Circumference of the wheel, C = 2 R = 2 2 = 4 m Number of revolutions completed, N = s C = 200 4 = 50 Answer: 50