<h2>
Answer:</h2>
8.75rad/s²
<h2>
Explanation:</h2>
The tires of the motorcycle undergo a rolling motion. Therefore, the tangential acceleration, , of the tires is equal to their linear acceleration, a. i.e
= a --------------(i)
But, the tangential acceleration, , is the product of the angular acceleration, , and the radius of the each of the tires. i.e
= r ------------(ii)
<em>Combine equations (i) and (ii) as follows;</em>
a = r --------------(iii)
<em>Also, the linear acceleration, a, is given by;</em>
a = ------------------(iv)
Where;
v = final linear speed of the tire
u = initial linear speed of the tire
t = time taken for the motion
Combine equations iii and iv as follows;
= r ------------------(v)
<em>From the question;</em>
v = 24.8m/s
u = 0 (since the motorcycle accelerates from rest)
t = 9.87s
r = 0.287m
<em>Substitute these values into equation (v) as follows;</em>
= 0.287
= 0.287
2.51 = 0.287
=
= 8.75rad/s²
Therefore, the angular acceleration of each tire is 8.75rad/s²