Answer
$v = 8.13~mi/s$
Work Step by Step
Jupiter orbits through an angle of $2\pi$ radians in 11.86 years. We can find the angular speed:
$\omega = \frac{\theta}{t}$
$\omega = \frac{2\pi~rad}{11.86~yrs}$
$\omega = 0.5298~rad/yr$
We can find the linear speed in miles per year:
$v = \omega ~r$
$v = (0.5298~rad/yr)(483,800,000~mi)$
$v = 256,300,000~mi/yr$
We can convert the linear speed to units of miles per second:
$v = 256,300,000~mi/yr\times \frac{1~yr}{365\cdot 24\cdot 3600~s}$
$v = 8.13~mi/s$
