Question

a car accelerates uniformly from rest to a speed of 16.5 m/s in 8.9 s. the diameter of the tire is 70.5 cm. find the number of revolutions the tide makes during the motion, assuming no sloping

A car accelerates rest and reaches a speed of 16.5 m/s in 8.9 s. The diameter of a tire is 70.5 cm uniformly from Find the number of revolutions the tire makes during this motion, assuming no slip- ping. Answer in units of r ev.

Answer 1

In this problem we will use concepts of motion in straight line and a little bit circular motion.

We know, v = u + at v = 1.65 m/s, u = 0, t = 8.9 s a = v minus u/t v rightarrow final speed u rightarrow initial speed a rightarrow acceleration t rightarrow time a = 16.5 minus 0/8.9 a = 1.85 m/s^2 Also, s = ut + 1/2 at^2 s = (0) (8.9) + 1/2 (1.85) (8.9)^2 s = 73.425 theta = s/R, R rightarrow radius, R = 0.3525 m = 73.425/0.3525 = 208.3 radians Number of revolution = theta/2 phi = 33.15 revolutions