# I Is F = ma the generalized force equation?

1. Mar 11, 2016

It just seems odd that the force on an object goes based on the second time derivative of its position vector. I understand that this is what is observed through experiment, but is this only for certain types of situations? Is the acceleration only some kind of low-order approximation of a particle's true trajectory due to forces, which also involve higher order time derivatives that are normally neglected?

2. Mar 11, 2016

### andrewkirk

No it's not an approximation, and it applies to all situations. The amounts involved (F and a) are instantaneous. The force F can vary over time and often does. In that case the third time derivative of position, and possibly higher derivatives too, will be nonzero. But the equation F=ma will hold at all times.

By the way, the third derivative is called jerk and the fourth derivative is jounce. They have other, equally colourful alternative names as well.

3. Mar 11, 2016

### Qwertywerty

Not in this sense; however, the actual equation for force is -
$F$ = $\frac {dp} {dt}$

We generalize this as $F = ma$. So to sum up, it is not an approximation in the sense you are considering. Hope this helps.

P.S. My first use of LaTex!