Velocity:

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

**1)**

From the given position, the velocity is:

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

The position of a particle is given by the function *x*=(2*t*^{3}−9*t*^{2}+12)m, where *t* is in s.

1.) At what time or times is *v*x = 0m/s?

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

Frequently Asked Questions

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 Position Functions and Instantaneous Velocity concept. You can view video lessons to learn Position Functions and Instantaneous Velocity. Or if you need more Position Functions and Instantaneous Velocity practice, you can also practice Position Functions and Instantaneous Velocity practice problems.