Position Functions and Instantaneous Velocity Video Lessons

Concept

# Problem: The position of a particle is given by the function x=(2t3−9t2+12)m, where t is in s.1.) At what time or times is vx = 0m/s?2.) What is the particle's position at this times?

###### FREE Expert Solution

Velocity:

$\overline{){{\mathbf{v}}}_{{\mathbf{x}}}{\mathbf{=}}\frac{\mathbf{d}\mathbf{x}}{\mathbf{d}\mathbf{t}}}$

1)

From the given position, the velocity is:

$\begin{array}{rcl}{\mathbf{v}}_{\mathbf{x}}& \mathbf{=}& \frac{\mathbf{d}}{\mathbf{d}\mathbf{t}}\mathbf{\left(}\mathbf{2}{\mathbf{t}}^{\mathbf{3}}\mathbf{-}\mathbf{9}{\mathbf{t}}^{\mathbf{2}}\mathbf{+}\mathbf{12}\mathbf{\right)}\\ & \mathbf{=}& \mathbf{6}{\mathbf{t}}^{\mathbf{2}}\mathbf{-}\mathbf{18}\mathbf{t}\end{array}$

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###### Problem Details

The position of a particle is given by the function x=(2t3−9t2+12)m, where t is in s.

1.) At what time or times is vx = 0m/s?

2.) What is the particle's position at this times?