How does distance an speed (rather than displacement and velocity) generalize to higher order derivatives?

Question

I'm a high schooler currently taking AP Physics C and during our review of kinematics, our teacher brought up the difference between speed and velocity. That is, speed is a scalar while velocity is a vector. So that made me wonder, is there a scalar version of higher-order derivatives? For further clarification, look at the table below:

Order     Vector           Scalar
0th       Displacement     Distance
1st       Velocity         Speed
2nd       Acceleration     ???
3rd       Jerk             ???

I'm curious about what would fit under those two question marks (or if they even have a name.)

Ok wow, I have no idea how I missed that. I guess this technically isn't a double post because I also asked about jerk, but that more or less answered my question. If we don't have one for acceleration then we don't have one for jerk. Thanks for the reply! — Snacc, Aug 27 '20 at 16:36
Don't forget the even higher order derivatives of Snap, Crackle and Pop. — JAlex, Aug 28 '20 at 21:05

score 1 · Accepted Answer · answered Aug 27 '20 at 16:31

1

As far as I know, the scalar version of acceleration, $|\mathbf a|$, does not have a special name. You would just say “acceleration”, and it would be understood by the context whether you are talking about a vector or a scalar. Same with jerk.

answered Aug 27 '20 at 16:31

Gilbert

11,877

More like "acceleration magnitude" which makes it clear, but often the "magnitude" is silent :-) – JAlex Aug 28 '20 at 21:03
@JAlex yes, good point. – Gilbert Aug 29 '20 at 02:32

How does distance an speed (rather than displacement and velocity) generalize to higher order derivatives?

1 Answers1