Aparticle moves along a circular path with radius 3 centimeters. the particle has an angular velocity of 3π/4 radians per second. what is the length of the arc, in centimeters, generated after 5 seconds? round your answer to the nearest tenth.

The first thing we must do in this case is to find the angle.
 For this, we have by definition:
 theta = w * t
 Where,
 theta: angle
 w: angular speed
 t: time
 Substituting the values we have:
 theta = (3π / 4) * (5)
 theta = (15π / 4)
 Then, the arc length will be:
 S = theta * R
 where,
 R: radio
 Substituting:
 S = (15π / 4) * (3)
 S = (45π / 4) cm
 
 The length of the arc, in centimeters, generated after 5 seconds is:
 S = (45π / 4) cm