# Math Help - Position of function at Rest

1. ## Position of function at Rest

Post of a function is s = t^3 - 6t^2 + 9t + 1

When is the particle at rest?

Can someone do a step by step for me...I have a test soon so I kinda just need to know.

2. Originally Posted by Dickson
Post of a function is s = t^3 - 6t^2 + 9t + 1

When is the particle at rest?

Can someone do a step by step for me...I have a test soon so I kinda just need to know.
The particle is at rest when the velocity is 0.

$v = \frac{ds}{dt} = 3t^2 - 12t + 9$

$0 = 3t^2 - 12t + 9$

$0 = 3t^2 - 9t - 3t + 9$

$0 = 3t(t - 3) - 3(t - 3)$

$0 = (t - 3)(3t - 3)$

The particle is at rest at $t = \{1, 3\}$.

3. Thanks a lot