# 3rd derivative name

#### bomba923

Although my notation is likely incorrect,

Momentum =
$$m\frac{{dx}}{{dt}} = m \cdot v$$

Force =
$$m\frac{{d^2 x}}{{dt^2 }} = m\frac{{dv}}{{dt}} = m \cdot a$$

Then,
$$m\frac{{d^3 x}}{{dt^3 }} = m\frac{{d^2 v}}{{dt^2 }} = m\frac{{da}}{{dt}}$$

But what would/do you call the $$m\frac{{da}}{{dt}}$$ ?

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#### rick1138

Don't know the answer in this context, but the derivative of acceleration is called jerk.

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#### bomba923

Well, my question is what is the name of mass*(da/dt); exactly what physical quantity does it represent (is it a useful physical quantity)?
From that, i think, i can give it a name---but if it already has one,

*What would/do we call the product represented by mass*(da/dt) ?

#### Claude Bile

It is just the first time derivative of Force $\frac{dF}{dt}$ (which is also the second time derivative of momentum), which is what the link robphy supplied in his post refers to.

It should be pointed out that using the word 'Yank' to represent this quantity is by no means official, it is more of a tongue in cheek proposition.

Claude.

#### bomba923

Ahh--that's right !

Yank =
$$m\frac{{da}}{{dt}}$$

#### AikenDrum

I can only say that its the quantity of "Yank" that makes you sick in a rollercoaster, because uniform acceleration doesn't disturb our senses very much...

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