A particle 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.
Accepted Solution
A:
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 Answer: The length of the arc, in centimeters, generated after 5 seconds is: S = (45π / 4) cm