What is second cubed?

[seriously disabled]

What is second cubed s^3 as in the wikipedia article?

 

http://en.wikipedia.org/wiki/Volt

[ajb]

[math]seconds \times seconds \times seconds[/math] as in units of time.

[seriously disabled]

[math]seconds \times seconds \times seconds[/math] as in units of time.

 

I know but what does it mean?

[ajb]

I know but what does it mean?

 

mean in what sense?

 

It is there because a volt is a SI derived unit.

[seriously disabled]

mean in what sense?

 

It is there because a volt is a SI derived unit.

 

I still don't get what the physical meaning of cubic second is.

[ajb]

It comes about because of the definitions and fundamental units. I would not think of it as "a cube in time" if that is what you mean.

[seriously disabled]

It comes about because of the definitions and fundamental units. I would not think of it as "a cube in time" if that is what you mean.

 

So how should I think of this?

[ajb]

I'd think of it as "book keeping". I don't know if anyone else here has different ways to think of things like this.

[J.C.MacSwell]

It is common in the inverse.

 

velocity in meters per second

 

acceleration in meters per second squared or per second per second

 

jerk (change in acceleration) in meters per second cubed or per second per second per second

[seriously disabled]

It is common in the inverse.

 

velocity in meters per second

 

acceleration in meters per second squared or per second per second

 

jerk (change in acceleration) in meters per second cubed or per second per second per second

 

Oh nice. Now you made it clear to me.

 

Thanks!

[Mudbird]

How would you use this in a kinematic equation? For example if height (x) is given by a constant times seconds-cubed, and an object is dropped from height x at time t, how do you figure out its falling time? If acceleration is not constant, then what is it? Thanks.

[Bignose]

How would you use this in a kinematic equation? For example if height (x) is given by a constant times seconds-cubed, and an object is dropped from height x at time t, how do you figure out its falling time? If acceleration is not constant, then what is it? Thanks.

 

I think that what you are asking here is imprecise.

 

However, if you are asking how, if given a specified jerk, how would you find the position as a function of time? You would integrate the jerk with respect to time three times. You will need 3 initial/boundary conditions.

 

velocity = [math] v = \frac{dx}{dt}[/math]

 

acceleration = [math] a = \frac{dv}{dt} = \frac{d}{dt} \frac{dx}{dt}[/math]

 

jerk = [math] j = \frac{da}{dt} = \frac{d}{dt} \frac{d}{dt} \frac{dx}{dt}[/math]

[CaptainPanic]

The second x second x second in itself means very little.

 

But in combination with other things it can be useful, like Bignose explained in the post just above this one.

 

Typically, the second x second x second, and all kinds of other weird units are found in constants and in intermediate solutions or derivations. The final outcome of any calculation will be something tangible again.

 

Take for example the Stefan-Boltzmann constant:

[math]\sigma = 5.670 400(40) \times 10^{-8}\ \textrm{W}\,\textrm{m}^{-2}\,\textrm{K}^{-4}.[/math]

It has weird units that mean little to me.

If you take the unit apart and only look to he Kelvin to the power 4, it means even less.

 

But in combination with a formula, it is correct and necessary.

[swansont]

The second x second x second in itself means very little.

 

But in combination with other things it can be useful, like Bignose explained in the post just above this one.

 

Typically, the second x second x second, and all kinds of other weird units are found in constants and in intermediate solutions or derivations. The final outcome of any calculation will be something tangible again.

 

Take for example the Stefan-Boltzmann constant:

[math]\sigma = 5.670 400(40) \times 10^{-8}\ \textrm{W}\,\textrm{m}^{-2}\,\textrm{K}^{-4}.[/math]

It has weird units that mean little to me.

If you take the unit apart and only look to he Kelvin to the power 4, it means even less.

 

But in combination with a formula, it is correct and necessary.

 

Right, because it turns out that radiation heat transfer scales with T^4. Nonlinear processes will often end up having constants with weird units.

 

Context is everything.

 

(I like the S-B, because it's easy to remember. 5678)