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# Problem: A particle is moving in a circle of radius 2 meters according to the relation θ = 3t2 + 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

###### FREE Expert Solution

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:

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

Power rule of derivation:

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

Relationship between linear and roational:

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

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###### Problem Details

A particle is moving in a circle of radius 2 meters according to the relation θ = 3t2 + 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

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Converting Between Linear & Rotational concept. You can view video lessons to learn Converting Between Linear & Rotational. Or if you need more Converting Between Linear & Rotational practice, you can also practice Converting Between Linear & Rotational practice problems.