# A car with 62 cm diameter tires accelerates uniformly from rest to 20m/s in 10s. How many times does each tire rotate?Thanks a lot in advance

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Using laws of linear motion;

v = u+at

20 = 0+a*10

a = 2 m/s^2

For angular and linear motion;

a = ralpha

alpha = a/r

alpha = 2/((62/100)/2) = 200/31rad/s^2

From angular motion;

theta = omega*t+1/2*alpha*t^2

theta = 0+1/2*200/31*10^2

theta = 322.58 rad

One rotation of tire covers 2pi radians.

The rotations that tire had = 322.58/(2pi) = 51.34

So the tyre has rotated 51.34 times. In other word the tyre had 51 complete rotation in 10 seconds.

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