Physics

Problem

3. A particle is moving in a circle of radius 2 meters according to the relation

\theta=3 t^{2}+2 t

, where

\theta

is measured in radians and

t

in seconds. The speed of the particle at

t=4

seconds is (A)

13 \mathrm{~m} / \mathrm{s}

(B)

16 \mathrm{~m} / \mathrm{s}

(C)

26 \mathrm{~m} / \mathrm{s}

(D)

52 \mathrm{~m} / \mathrm{s}

(E)

338 \mathrm{~m} / \mathrm{s}

(A)

13 \mathrm{~m} / \mathrm{s}

(B)

16 \mathrm{~m} / \mathrm{s}

(C)

26 \mathrm{~m} / \mathrm{s}

(D)

52 \mathrm{~m} / \mathrm{s}

(E)

338 \mathrm{~m} / \mathrm{s}

Intuitive explanation

Circular motion speed depends on how fast the particle sweeps through angle—that's angular velocity $\omega$ . Find $\omega$ by differentiating the angle equation with respect to time, evaluate it at $t=4$ s, then convert to linear speed using $v = \omega r$ , where $r$ is the radius.

Intuitive explanation

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