Solve the problem.
-An object is traveling around a circle with a radius of 10 meters. If in 15 seconds a central angle of 3 radians is swept out, what is the linear speed of the object?
A) $2 \mathrm {~m} / \mathrm { sec }$
B) $\frac { 1 } { 3 } \mathrm {~m} / \mathrm { sec }$
C) $\frac { 2 } { 3 } \mathrm {~m} / \mathrm { sec }$
D) $3 \mathrm {~m} / \mathrm { sec }$

Question

Solve the problem.
-An object is traveling around a circle with a radius of 10 meters. If in 15 seconds a central angle of 3 radians is swept out, what is the linear speed of the object? 
A) $2 \mathrm {~m} / \mathrm { sec }$
B) $\frac { 1 } { 3 } \mathrm {~m} / \mathrm { sec }$
C) $\frac { 2 } { 3 } \mathrm {~m} / \mathrm { sec }$
D) $3 \mathrm {~m} / \mathrm { sec }$

Quizplus · Accepted Answer

The linear speed $v$ of an object moving along a circular path is given by $v = \frac{s}{t}$, where $s$ is the arc length and $t$ is the time. The arc length $s$ can be calculated using the formula $s = r\theta$, where $r$ is the radius and $\theta$ is the central angle in radians. Here, $r = 10$ meters and $\theta = 3$ radians. So, $s = 10 \times 3 = 30$ meters. Given $t = 15$ seconds, the linear speed $v = \frac{30}{15} = 2 \mathrm {~m} / \mathrm { sec }$.

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