#### Answer

The suitcase is dragged a distance of 0.68 meters before it is moving smoothly on the belt.

#### Work Step by Step

The force of kinetic friction will bring the suitcase up to a speed of 2.0 m/s. We can find the magnitude of acceleration.
$F_f = ma$
$mg~\mu_k = ma$
$a = g~\mu_k$
$a = (9.80~m/s^2)(0.30)$
$a = 2.94~m/s^2$
We can find the distance the suitcase moves while the force of friction brings the suitcase up to a speed of 2.0 m/s.
$x = \frac{v_f^2-v_0^2}{2a}$
$x = \frac{(2.0~m/s)^2-0}{(2)(2.94~m/s^2)}$
$x = 0.68~m$
The suitcase is dragged a distance of 0.68 meters before it is moving smoothly on the belt.