R = 2 m
α = 0.30 rad/s2
\(\vartheta\) = 7m/s
We use the formula for kinematics of rotational motion to solve
\(\omega^2-\omega_0\,^2\) = 2α(θ - θ0)
∵ \(\omega_0 - 0 \)
\(\omega^2 = 2 \times0.30(\theta -\theta_0)\)
∵ \(\vartheta = r\omega\)
\(\omega = \frac{\vartheta}{r}\)
⇒ \(\frac72 = 3.5 \) rad/s
(3.5)2 = 2 x 0.30 (θ - θ0)
(θ - θ0) = \(\frac{12.25}{0.6}\)
(θ - θ0) = 20.41 rad
Then
S = rθ
S = 2 x 20.41
S = 40.83 m