Is F = ma the generalized force equation?

[TheCanadian]

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?

 

[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.

 

[Qwertywerty]

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?

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!