Torque/Rotation Problem

1. The problem statement, all variables and given/known data

A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, as shown in the figure (see the figure (Figure 1) ). The pulley is a uniform disk with mass 11.8kg and radius 55.0cm and turns on frictionless bearings. You measure that the stone travels a distance 12.7m during a time interval of 2.80s starting from rest.

Find the mass of the stone.

Find the tension in the wire.

Figure 1

2. Relevant equations

Work Kinetic Energy Theorem

3. The attempt at a solution

[itex]a_{stone}=\frac{2\Delta X}{t^2}=3.24[/itex]
[itex]\Delta K = W_{wheel} + W_g=0[/itex]
[itex]\Delta K = \frac{I\omega_f^2}{2}+W_g[/itex]
[itex]\omega = \alpha t [/itex] ??

And that’s where I got stuck, I don’t know how to derive the final angular velocity

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