# 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:

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

100% (92 ratings) ###### 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