Answer
The pebble's speed is 5.7 m/s and the pebble's acceleration is $107~m/s^2$
Work Step by Step
The wheel rotates 3 revolutions each second. We can find the angular speed of the wheel as:
$\omega = (2\pi~rad/rev)(3~rev/s)$
$\omega = 6\pi~rad/s$
We can find the speed of the pebble as:
$v = \omega ~r$
$v = (6\pi~rad/s)(0.30~m)$
$v = 5.7~m/s$
We can find the centripetal acceleration of the pebble as:
$a_c = \omega^2~r$
$a_c = (6\pi~rad/s)^2(0.30~m)$
$a_c = 107~m/s^2$
The pebble's speed is 5.7 m/s and the pebble's acceleration is $107~m/s^2$.
