The wheel turns through an angle of 11 rad in the first 2.0s.
Step-by-step explanation:
To find the angle through which the wheel turns in the first 2.0s, we can use the formula:
θ = ωi*t + (1/2)*α*t^2
where:
θ = angle of rotation
ωi = initial angular velocity
α = angular acceleration
t = time
Plugging in the given values:
ωi = 1.0 rad/s
α = 4.5 rad/s^2
t = 2.0s
θ = (1.0 rad/s * 2.0s) + (1/2 * 4.5 rad/s^2 * (2.0s)^2)
θ = 2.0 rad + 9.0 rad
θ = 11 rad
Therefore, the wheel turns through an angle of 11 rad in the first 2.0s.