Velocity:

$\overline{){\mathbf{v}}{\mathbf{=}}\sqrt{{{\mathbf{v}}_{\mathbf{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbf{v}}_{\mathbf{y}}}^{\mathbf{2}}}}$

The x-component of velocity, v_{x}

$\begin{array}{rcl}{\mathbf{v}}_{\mathbf{x}}& \mathbf{=}& \frac{\mathbf{d}\mathbf{x}}{\mathbf{d}\mathbf{t}}\\ & \mathbf{=}& \frac{\mathbf{d}}{\mathbf{d}\mathbf{t}}\mathbf{(}\mathbf{12}{\mathbf{t}}^{\mathbf{3}}\mathbf{-}\mathbf{2}{\mathbf{t}}^{\mathbf{2}}\mathbf{)}\end{array}$

v_{x} = 36t^{2} - 4t

The y-component of velocity, v_{y}

$\begin{array}{rcl}{\mathbf{v}}_{\mathbf{y}}& \mathbf{=}& \frac{\mathbf{dy}}{\mathbf{dt}}\\ & \mathbf{=}& \frac{\mathbf{d}}{\mathbf{dt}}\mathbf{(}\mathbf{12}{\mathbf{t}}^{\mathbf{2}}\mathbf{-}\mathbf{2}\mathbf{t}\mathbf{)}\end{array}$

v_{y}_{ }= 24t - 2

A particle's trajectory is described by x =(12t^{3}−2t^{2})m and y =(12t^{2}−2t)m, where t is in s.

Part B What is the particle's speed at t=5.0s ? Express your answer using two significant figures. v = m/s

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