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The radius of a body moving in a circle with constant angular velocity is given by $r=$ $4 \mathrm{t} 2$, with respect to time. What is the magnitude of the tangential velocity at $t=2 \mathrm{~s}$, if the angular velocity is $7 \mathrm{rad} / \mathrm{s}$ ?
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$112$
Given, $r=4 \mathrm{t}^2$, and angular velocity, $\boldsymbol{\omega}=7$ $\mathrm{rad} / \mathrm{s}$
We know that tangential velocity, $v=r \omega$
At $t=2 s, r=4(2)^2=16 \mathrm{~m}$
Substituting the given values, $v=16 \times 7=$ $112 \mathrm{~m} / \mathrm{s}$
Therefore, the magnitude of the tangential velocity at $\mathrm{t}=2 \mathrm{~s}$ is $112 \mathrm{~m} / \mathrm{s}$.
We know that tangential velocity, $v=r \omega$
At $t=2 s, r=4(2)^2=16 \mathrm{~m}$
Substituting the given values, $v=16 \times 7=$ $112 \mathrm{~m} / \mathrm{s}$
Therefore, the magnitude of the tangential velocity at $\mathrm{t}=2 \mathrm{~s}$ is $112 \mathrm{~m} / \mathrm{s}$.
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