# Question #092ca

Apr 18, 2017

The linear speed is $= 48.75 m {s}^{-} 1$
The centripetal acceleration is $= 31.69 m {s}^{-} 2$
The tangential acceleration is $= 17.25 m {s}^{-} 2$

#### Explanation:

radius is $r = 75 m$

angular speed is $\omega = 0.65 r a {\mathrm{ds}}^{-} 1$

angular acceleration is $\alpha = 0.23 r a {\mathrm{ds}}^{-} 2$

The linear speed is

$v = \omega r$

$= 0.65 \cdot 75 = 48.75 m {s}^{-} 1$

The centripetal acceleration is

${a}_{c} = {v}^{2} / r = {\omega}^{2} r$

$= 0.65 \cdot 0.65 \cdot 75 = 31.69 m {s}^{-} 2$

The tangential acceleration is

${a}_{t} = \alpha r$

$= 0.23 \cdot 75 = 17.25 m {s}^{-} 2$