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22 October, 14:57

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.

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  1. 22 October, 18:01
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    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
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