This is a calculus problem because we are given a position funtion. The angular position is given in terms of θ. To get the angular velocity function, we need the relationship between angular position and angular velocity.

Motion with Calculus:

$\mathit{\theta}\begin{array}{c}{\mathbf{\leftarrow}}\\ {\mathbf{\to}}\end{array}\underset{\frac{\mathbf{d}}{\mathbf{d}\mathbf{t}}}{\overset{{\mathbf{\int}}{\mathbf{d}}{\mathbf{t}}}{\mathbf{\omega}}}\begin{array}{c}{\mathbf{\leftarrow}}\\ {\mathbf{\to}}\end{array}\mathit{\alpha}$ where θ is the position, ω is the angular velocity, and α is angular acceleration.

Power rule of derivation:

$\overline{)\frac{\mathit{d}}{\mathit{d}\mathit{t}}\mathbf{\left(}{\mathit{x}}^{\mathit{n}}\mathbf{\right)}{\mathbf{=}}{\mathit{n}}{{\mathit{x}}}^{\mathit{n}\mathbf{-}\mathbf{1}}}$

Relationship between linear and roational:

$\overline{){\mathbf{v}}{\mathbf{=}}{\mathbf{r}}{\mathbf{\omega}}}$

A particle is moving in a circle of radius 2 meters according to the relation θ = 3t^{2} + 2t, where θ is measured in radians and t in seconds. The speed of the particle at t = 4 seconds is

(A) 13 m/s

(B) 16 m/s

(C) 26 m/s

(D) 52 m/s

(E) 338 m/s

Frequently Asked Questions

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