From the information given,
initial speed, u = 0 because the car started from rest
Final speed, v = 32.1 m/s
time, t = 13.8
We would find the distance covered by the car, d by applying one of Newton's formula of motion which is expressed as
d = 1/2(u + v)t
By substituting the values into this formula, we have
d = 1/2(0 + 32.1)13.8
d = 221.49 m
Recall,
d = θR
where
θ is the angular displacement
R is the radius
From the information given,
R = 84.7 cm
We would convert from cm to m.
recall,
100 cm = 1m
84.7 cm = 84.7/100 = 0.847m
Substituting R = 0.847 and d = 221.49 into the formula, it becomes
221.49 = 0.847θ
Dividing both sides of the equation by 0.332, we have
θ = 221.49/0.847
θ = 261.5 radians
1 radian = 0.159 revolutions
261.5 radians = 261.5 x 0.159
= 41.6 revolutions
Number of revolutions = 41.6