Dynamic of Rotational motion

Question

A wheel rotates for 5sec with a constant angular acceleration and describe a displacement of 100radian, it is then rotates with a constant angular velocity in the next 5sec and describe a displacement of of 80 radians. Find

1) initial angular velocity.   Answer (24rad/s)

2) final angular velocity (16rad/s)

3) angular acceleration of the wheel(1.6rad/s²)

Hint: simultaneous equation.

Please I just need a clear explanation of the equations to use.

Answer 1

As we know that the wheel rotate for 5 s with constant angular acceleration

so we have

θ \(=\frac{\omega+\omega_0}2t\)

100 \(=\frac{\omega+\omega_0}2(5)\)

ω+ω₀ = 40

now we know that after this it rotate with constant angular speed for t = 5 s

so now we have

θ = ωt

80 = ω(5)

ω = 16 rad/s

now we have

16+ω₀ = 40

ω₀ = 24 rad/s

now angular acceleration is given as

α \(=\frac{\omega+\omega_0}t\)

α \(\frac{16-24}5\)

α = -1.6 rad/s²