A car starts from rest and then accelerates uniformly to a linear speed of 13 m/

Question

A car starts from rest and then accelerates uniformly to a linear speed of 13 m/s in 43 s. If the tires have a radius of 22 cm, what are the following?
(a) the average linear acceleration of a tire
1 m/s2

(b) the angular acceleration of a tire
2 rad/s2

(c) the angular displacement of a tire from t = 0 to t = 43 s
3 rad

(d) the total distance traveled by a point on the edge of a tire (Ignore the linear motion.)
4 m

Explanation / Answer

since v0= 0 22 cm => 22/2 => 11 cm => 0.11 m b) angular acceleration (v - vo) / Rt = 13 / 0.11* 43 = 2.748 rad/s^2 c) angular displacement = 1/2 angular acceleration* t^2 = 0.5 * 2.748 * (43)^2 =2540 rad d) distance = 2540 * 0.11 = 279.4 m

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