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If an object covers d distance at the arc of the circle, it creates θ angle at its center and it relates to the formula:

d = rθ

Here, r = radius of the circle.

Also, θ = ωt

Where, ω = angular velocity

t = time taken.

Solution: Given that,

Angular velocity = 2.45 rad/s

Angular acceleration = 7.5 rad/s^2

Time = 12 sec

As we know that, in linear motion

d = vt + ½ at^2

We can use the same equation in circular motion,

θ = ωt + ½ αt^2

= (2.45)(12) + ½ (7.5)(12)^2

= 569.4 radians

Displacement, d = 25 m

Radius of the circle, r = 5 m

So that, θ = d/r

= 25/5 = 5 radians.