Question

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.

Answer 1

35.3 cm would actually be the correct answer.

Your question:

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.

Answer 2

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