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

After 5 s, the particle traverses a path subtended by an angle of

(3π/4 rad/s) (5 s) = 15π/4 rad

Now, 15π/4 rad = 15/8 * 2π rad, so the arc has a length equal to 15/8 of the circumference of the path:

15/8 * 2π * (3 cm) = 45π/4 cm ≈ 35.3 cm