Use the exact values you enter in previous answer(s) to make later calculation(s

Question

Use the exact values you enter in previous answer(s) to make later calculation(s). A car starts from rest and then accelerates uniformly to a linear speed of 16 m/s in 44 s. If the tires have a radius of 27 cm, what are the magnitudes of the average linear acceleration of a tire, the angular acceleration of a tire, the angular displacement of a tire from t = 0 to 44 s, and the total distance traveled by a point on the edge of a tire? (a) the average linear acceleration of a tire m/s2 (b) the angular acceleration of a tire rad/s2 (c) the angular displacement of a tire from t = 0 to 44 s rad (d) the total distance traveled by a point on the edge of a tire (Ignore the linear motion.) m

Explanation / Answer

given that intial speed u=0

final speed v=16m/s

time taken t=44s

radius f the tire is r=0.27m

a) from kinematic relation

v=u+at

16=0+a*44

a=16/44

=0.3636m/s^2

b) angular accleration =a/r

=0.3636/0.27

=1.347 rad/s^2

from the kinematic relation

linear distance travelled

s=ut+1/2at^2

=1/2*0.3636*44^2

=351.96m

c) the angular displacement is

=s/r

=351.9648/0.27

=1303.57 rad

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