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.

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