# Thread: Particle movement: displacement & aver. velocity

1. ## Particle movement: displacement & aver. velocity

A particle moves along a vertical coordinate axis so that its position is given by the function:

S(t) = 1/3 t^3 - 3t^2 + 8t - 4.

Find displacement during first 6 seconds. Find average velocity during first 6 seconds.

A little help? Thanks.

2. ## Re: Particle movement: displacement & aver. velocity

Originally Posted by snickerdoodle27
A particle moves along a vertical coordinate axis so that its position is given by the function:

S(t) = 1/3 t^3 - 3t^2 + 8t - 4.

Find displacement during first 6 seconds. Find average velocity during first 6 seconds.

A little help? Thanks.
you're expected to know the definitions of displacement and average velocity ...

displacement, $\Delta s = s(t_f) - s(t_0)$

average velocity, $\bar{v} = \frac{\Delta s}{\Delta t}$

3. ## Re: Particle movement: displacement & aver. velocity

Thanks! So it displaces 12 m in 6 sec, thereby making its aver. velocity 2 m/s.

And one more question: when is the particle moving downward? How do I find that analytically?

4. ## Re: Particle movement: displacement & aver. velocity

Originally Posted by snickerdoodle27
Thanks! So it displaces 12 m in 6 sec, thereby making its aver. velocity 2 m/s.

And one more question: when is the particle moving downward? How do I find that analytically?
the particle's direction of motion is determined by the sign of its velocity. velocity is the time derivative of position ...

$v(t) = s'(t)$

5. ## Re: Particle movement: displacement & aver. velocity

Originally Posted by skeeter
the particle's direction of motion is determined by the sign of its velocity. velocity is the time derivative of position ...

$v(t) = s'(t)$
so basically you find at what times the velocity is equal to zero... but then what? Don't you have to look at a graph then to see if the time between those two points is below/above the x-axis?

6. ## Re: Particle movement: displacement & aver. velocity

Originally Posted by snickerdoodle27
so basically you find at what times the velocity is equal to zero... but then what? Don't you have to look at a graph then to see if the time between those two points is below/above the x-axis?
you check the sign of the velocity for any time between the specific times it is zero ... it has to be either positive or negative for all times in that interval, correct?

7. ## Re: Particle movement: displacement & aver. velocity

Originally Posted by skeeter
you check the sign of the velocity for any time between the specific times it is zero ... it has to be either positive or negative for all times in that interval, correct?
Thank you skeeter!